This is a question that I was wondering about since I was introduced to the Borg in Star Trek: The Next Generation.
Why do the Borg want to assimilate every planet in the universe?
It started out as a race who used technology to increase perfection in itself. Perfection involved cooperation and communication and community. These were carried to pathological extremes, then they decided to extend perfection into the universe. It's a perfect example of too much of something good being bad.
The Borg consider all biological lifeforms to be inherently flawed, and see themself as the solution to this. It makes sense from the Borg point of view, leading the Borg to be aggressively territorial. Everything outside of the Borg is an unknown variable and therefore likely to interfere in their march to perfection. So a species is either a source of drones for expansion, or an enemy to be conquered and cleared away.
The strength of the Borg in terms of numbers as well as offensive and defensive capabilities is repeatedly represented as far superior than many other groups in Star Trek (thanks to their practice of assimilating anyone with technology that would benefit them). For example, even a single Borg cube is a formidable threat at the Battle of Wolf 359, killing 11,000 and destroying 39 ships.
In Voyager it's clear that the Borg have their own territory, but Borg ships also show up throughout the show both before and after Voyager enters that territory. But they have the ability to travel so quickly using transwarp conduits that they could appear suddenly far outside of their own territory. In Voyager 6x19 a transwarp conduit is located less than a light year from Icheb's home planet, but Voyager's journey through Borg space was all the way back in season 3/4.
Thus it's clear that the Borg could expand their territory and assimilate almost any group, at least in the Delta Quadrant. They have the numbers, the strength, and the ability to travel anywhere. Yet they are clearly not doing that because otherwise you would have expected the Borg to be running rampant throughout the galaxy. Q says the Borg have been around for "thousands of centuries" (source).
Additionally, we see many times that the Borg completely ignore people they don't deem to be a threat. Again and again, in both TNG and Voyager, non-Borg are shown walking around on a Borg ship without triggering a defensive response as long as they aren't deemed to be a threat. The implication is that the Borg see themselves as so superior that people walking on their ships could be analogous to insects in your home in that you might ignore them as long as they aren't too much of a problem. The Borg see themselves as so powerful that trespassers on one of their ships aren't necessarily a problem, and they are obsessed with efficiency such that even if they do detect them they couldn't be bothered to do anything about it. That explanation doesn't always make much sense but that's what we're given.
We do know that the Borg are obsessed with perfection. In Voyager 4x21 "The Omega Directive", Seven of Nine is fascinated by the Omega particle because of her time as a Borg and its ability to form a perfect structure. Memory Alpha has an article on Borg philosophy which states:
The principal philosophy of the Borg Collective was a drive towards achieving a state of "perfection" for themselves and, in their view, all life
However, some species were deemed unworthy, such as the Kazon:
Their biological and technological distinctiveness was unremarkable; they were unworthy of assimilation
-- Seven of Nine, VOY 4x12 "Mortal Coil"
So while the Borg want to do a lot of assimilation there's clear evidence that they don't "want to assimilate every planet in the universe". They could have attacked far more worlds, far more often than they actually were shown to, and they frequently ignore essentially helpless targets that are either categorized as non-threatening or unworthy.
However, we also can't definitively say that the Borg don't want to assimilate everyone. It's possible that given enough time and barring (futile) resistance they would gladly assimilate everyone, even the unworthy, but constraints on resources and strategic considerations limit what they accomplish. But clearly they prioritize efficiency and expect a return on investment so to speak when they assimilate anyone into their collective.
I should note also that the conflict with Species 8472 indicate that the Borg sought to expand even outside of the universe, as the Fluidic Space Species 8472 came from was another dimension.