[im3w1l-alt]

If you let the number of objects to sort go to infinity while keeping size of objects in bits capped, then they will behave like integers.

[eru]

I thought more of being able to do bit manipulation or hashing etc on your keys. Those things don't necessarily require a fixed key length. (And in some languages, even integers don't have a fixed length.)

You are right in some sense, but you'd still have trouble implementing something like bucket sort in your setting, if all you have are comparisons.