The problem with this is that you may end up with a 3x3x3 cube that is not solvable. For instance, you can get a state where the entire cube is solved, except for two edges that need to swap locations. This isn't possible. In group theoretical language, only even permutations are possible. You can swap two _pairs_ of edges, but not just two edges.
When you end up in such an unsolvable 3x3x3 cube, you have to temporarily turn the inner layers of the cube and break apart the centers and edges you built in the first step, and then reassemble them again to a solvable 3x3x3 cube.
The hollow 3 has a similar problem. Because you can’t see the central piece there’s a way to rotate the core and a couple of edge pieces so they look like they violate parity.
(There is a very easy-to-remember algorithm that can be trivially executed by humans given here in a Mathologer video, with a time-code link to jump straight to it: https://youtu.be/MbonokcLbNo?si=ey8bv4T9KbDxgB7N&t=650 )
Another annoying thing about 4x4x4 compared to 5x5x5 is that you have two possible types of parity issues on the 4x4x4. On the 5x5x5, only one of these can occur.
Nevertheless, if you know how to solve a 3x3x3 and no bigger cube, a 4x4x4 is certainly the easiest next step.
https://ruwix.com/twisty-puzzles/bandaged-cube-puzzles/
in particular, "bandaged cubes" in which certain faces have fused blocks to limit your available moves, and "constrained cubes" in which certain faces can only rotate in one direction, and only by a certain amount.
https://www.rubiks.com/products/rubiks-impossible
Sticker sets are also available, like this one
Anything beyond 7x7x7 is pretty much the same. It's just more annoying, because the puzzle gets physically harder to handle, and because you have to do the tedious work of counting how many layers away from the centre a piece is. The 7x7x7 is the biggest cube used in official competitions, for a good reason.
The motivation for making enormous cubes like the 34x34x34 is just the engineering challenge, and breaking records. Nobody is going to want to solve such a thing, at least not more than once.