Whether you get 512 GB or just 128GB. Storage management is not something you can't escape. Eventually even 512GB will fill up. But just because they are filled up, does not mean they cannot be cleared up as well. Storage space, can be cleared, and a filled up storage space does not in any way indicate outgrowing of the device.
The iPad 2 is 8 year old hardware at this point. Crashes may be indeed due to lack of storage space, though the age of the device may also be a factor. One way to find out if its a storage space issue, is to delete some content from the iPad and make space. If still crashes with some free space available, then the iPad may have other issues. You do want to make sure there's at least 10% of free space at all times. For a 64GB iPad, that should be around 6 to 8GB of free space.
You can buy all the storage you want, but if you don't do normal storage management everything can get filled up. Downloading stuff without regard will eventually fill up even the largest storage capacities.
Without any storage management even 512 can be filled up pretty fast.
If you go to Settings->General->Storage and iCloud Usage you can see what is taking up the most space and deal with it.