They’d be vulnerable to external threats.
To begin with, fitting a portion of the wizarding population into a suitcase may not be a particularly good idea. Suitcases, in essence, are portable, and can be held shut.
“HOLD ON TINA as she hides on the bridge above them, peeking down.
NEWT (O.S.)
(to Jacob)
In you hop.
We see the case sitting alone below the bridge.
Tina quickly appears around the corner and hurriedly sits on the case. She closes the catches, looking shocked but determined.”
- Fantastic Beasts and Where to Find Them (The Original Screenplay)
This would leave any wizarding population inside the suitcase extremely vulnerable to external threats. Anyone outside of it could decide to move or destroy it without anyone inside knowing it. Newt carries his creatures in his case, but he does not leave it unattended for long. There is always someone around who is aware what is happening outside of his case.
“A particularly loud explosion in the distance. The city beneath them is starting to burn. Newt thrusts his case into Tina’s hands and takes a journal from his pocket.
NEWT
If I don’t come back, look after my creatures. Everything that you need to know is in there.”
- Fantastic Beasts and Where to Find Them (The Original Screenplay)
There is also the risk that something could happen in the place the suitcase is rested, like a fire or a hurricane, that could destroy the suitcase and everyone in it. Additionally, as Extension Charms do have limits, fitting the entire wizarding population would require several suitcases, not just one. As explained below, it would likely require at absolute minimum three thousand suitcases to contain the entire wizarding population. This means that wizards would have to ensure the safety of at least three thousand suitcases.
Extension Charms likely have their limits.
Though Extension Charms can greatly increase the capacity of an object, it does seem to have its limits. A writing by JKR states that theoretically, a hundred wizards could live in a toilet cubicle if they were sufficiently skilled at Extension Charms. As a hundred wizards living in a toilet cubicle is described as a theoretical case, only accomplishable by extremely skilled wizards, this would imply it is close to the bounds of what can be done with Extension Charms.
The Extension Charm (‘Capacious extremis!’) is advanced, but subject to strict control, because of its potential misuse. Theoretically, a hundred wizards could take up residence in a toilet cubicle if they were sufficiently adept at these spells; the potential for infractions of the International Statute of Secrecy are obvious. The Ministry of Magic has therefore laid down a strict rule that capacity-enhancement is not for private use, but only for the production of objects (such as school trunks and family tents), which have been individually approved for manufacture by the relevant Ministry Department.
- Extension Charms (wizardingworld.com)
Therefore, it would likely be beyond the capability of the Extension Charm to create a world substantial enough for the entire global population of wizards to all live in. There are at least a hundred thousand wizards in the global population, since one hundred thousand wizards usually attend the Quidditch World Cup. Therefore, the global wizarding population is likely much larger than that.
“The trouble is, about a hundred thousand wizards turn up to the World Cup, and of course we just haven’t got a magical site big enough to accommodate them all. There are places Muggles can’t penetrate, but imagine trying to pack a hundred thousand wizards into Diagon Alley or platform nine and three-quarters.”
- Harry Potter and the Goblet of Fire, Chapter 6 (The Portkey)
One hundred thousand wizards is just the number who are willing and able to attend the Quidditch World Cup. That doesn't account for wizards who do not like Quidditch, or were busy, or had other responsibilities, or could not afford the trip. The number in the total global population of wizards would be therefore at least somewhat higher, likely a large portion higher. After all, even though something like the soccer World Cup in the Muggle world is a very popular sporting event, only a small fraction of the total Muggle population attends it. Since it would take very skilled wizards to fit one hundred wizards in a toilet cubicle, it would likely be impossible to fit a number much greater than a hundred thousand wizards in a suitcase. It would likely not even be possible to fit the entire British Ministry of Magic in a suitcase, as there are quite a bit more than five hundred wizards in the British Ministry.
“Seats a hundred thousand,’ said Mr Weasley, spotting the awestruck look on Harry’s face. ‘Ministry task force of five hundred have been working on it all year.”
- Harry Potter and the Goblet of Fire, Chapter 8 (The Quidditch World Cup)
Since the British Ministry can have a task force of five hundred working on the Quidditch World Cup with enough people remaining for other functions, it must employ several more than that. Therefore, it has more than five times as many wizards as can be theoretically fit in a toilet cubicle, so just to fit the British Ministry would need more than five suitcases. Using a very conservative estimate of the global wizarding population at three hundred thousand, and considering that a suitcase (being smaller) would not hold more than a toilet cubicle, it would require three thousand suitcases to contain the entire wizarding population.
Societal functions would be difficult.
Additionally, if wizarding society was separated into groups that could fit in a suitcase, it would be difficult for the normal functions of society to continue. If each case contains one hundred wizards, from then on it would be nearly impossible for them to live as part of a larger society. The Ministry could theoretically fit into five suitcases, but then they would be cut off from the people they govern, and with no way of monitoring other suitcases, would be unable to stop crime. Wizards would have to separate into small villages containing everyone necessary for a small village to function. Each case would need, for example, its own governing body and at least one Auror. Anything that requires a large number of wizards to accomplish would become impossible. For example, the Quidditch World Cup could not continue in a society of suitcases.
“Seats a hundred thousand,’ said Mr Weasley, spotting the awestruck look on Harry’s face. ‘Ministry task force of five hundred have been working on it all year.”
- Harry Potter and the Goblet of Fire, Chapter 8 (The Quidditch World Cup)
This would be impossible to organize in a wizarding society split into groups in suitcases. A Ministry task force of five hundred would have nowhere to assemble, and there would be nowhere large enough to fit one hundred thousand wizards.
Some wizards are weary of hiding.
In addition, not all wizards agree that wizards should be forced into hiding from Muggles.
“GRAVES
(laughing bitterly)
A law that has us scuttling like rats in the gutter! A law that demands that we conceal our true nature! A law that directs those under its dominion to cower in fear lest we risk discovery! I ask you, Madam President—
(eyes flashing to all present)
—I ask all of you—who does this law protect? Us?
(gesturing vaguely to the No-Majs above)
Or them?
(smiling bitterly)
I refuse to bow down any longer.”
- Fantastic Beasts and Where to Find Them (The Original Screenplay)
Those who believe that wizards should not be forced into hiding from Muggles would certainly not agree that wizards should pack themselves up into suitcases to do so.
Some wizards might not want separation.
Additionally, there are certain wizards who might prefer living among Muggles even if they have to keep their magic secret rather than live among only wizards. Even after the Statute of Secrecy was signed, some wizards still chose to live in communities alongside Muggles.
“Upon the signature of the International Statute of Secrecy in 1689, wizards went into hiding for good. It was natural, perhaps, that they formed their own small communities within a community. Many small villages and hamlets attracted several magical families, who banded together for mutual support and protection. The villages of Tinworth in Cornwall, Upper Flagley in Yorkshire and Ottery St Catchpole on the south coast of England were notable homes to knots of wizarding families who lived alongside tolerant and sometimes Confunded Muggles. Most celebrated of these half-magical dwelling places is, perhaps, Godric’s Hollow, the West Country village where the great wizard Godric Gryffindor was born, and where Bowman Wright, wizarding smith, forged the first Golden Snitch.”
- Harry Potter and the Deathly Hallows, Chapter 16 (Godric’s Hollow)
Getting these wizards to agree to separate entirely from the Muggles is likely to be quite difficult, and any attempt to do so is likely to face fierce opposition.