As Daenerys lands at Dragonstone, it is a deserted place. Cersei could have captured the place or even destroyed it with wildfire. She already knew Dany was coming and she would station most probably at Dragonstone.
The analysis shown by TV show is wrong.
Jaime says Daenerys will land most probably on Dragonstone because of Deep water ports. That doesn't make any military sense, I'll explain why:
- The closest Westerosi port from Meereen is Planky town.
- It is a major port of Westeros and trading hub so naturally has Deep-Water ports.
- Dragonstone is very far up North, right in front of the King's Landing.
- The Dornish are Targaryen allies.
- The Tyrells, other Targaryen allies, border the Dornish.
- Two highways go from Dorne to KL. One from Prince's pass and one from the Boneway.
So Planky Town should have been the most obvious choice for landing zone.
Timing is everything in the war, Daenerys should have chosen the closest friendly port for landing which is Planky Town. She could easily land there, get her armies together, plan her moves, in a friendly port rather than sailing to parts unknown where she might fact resistance.
Dragonstone is a desolate rock with no strategic advantage other than presenting a base for a naval blockade of King's Landing. And it is very much up north, Why take the risk of maritime travel in notoriously stormy Narrow sea in Winter? Targaryen troops are most vulnerable when embarked.
Daenerys needed to connect with her allies. Those are Dornish and Tyrells. The Starry Sept, most prestigious sept in the country since destruction of Sept of Baelor is located in Old Town on Tyrell-Martell border. Aegon the Conqueror himself was crowned there. Daenerys could have done the same. A formal coronation and anointation to match unanointed Cersei would have been huge.
But because D&D wanted an emotional scene, they took Dany back to her birthplace and ancient seat of Targaryens. Reeeeeeeeeeee!
Now that my rant is over, coming back to your original question and playing along with D&D's rules, it would be because any resistance there would have been futile.
Crown did not have a Navy since the Battle of Blackwater bay. Who was going to ferry the occupation troops? There are no funds to raise new fleet anyways, The crown is bankrupt, the Lannister coffers are empty and the Ironbank is pissed because of Crown defaulting on Robert's debts.
And even if they somehow ferried troops across the gullet, to what end?
There would have been no prospect of relief once Daenerys had landed at Dragonstone and the men sent there would have been lost, men who would be needed to defend King's Landing in the coming weeks.
So it was much better to conserve your strength, let Daenerys take Dragonstone as there wasn't much they could do about it anyways, and then defend King's Landing, which itself is madness.
An even better approach would have been abandoning King's Landing and retreating to Casterly Rock. Visenya Targaryen took a look at the rock and thanked God that Lannisters had chosen to fight in the field instead of falling back to their great castle. But abandoning KL means abandoning the throne as well. There isn't much hope for Lannister cause anyways, what remains is, how much can they salvage from the situation?
As for destroying Dragonstone, cui bono? Who benefits? And not to mention, it is unlikely Cersei has that much Wildfire left, if any, or means to transport it to Dragonstone.