This is a great discussion.
It seems to me that a good part of the issue described above is not a numerical one (2^251 vs 2^256), it’s an “coding comfort one” (3 simple lines of codes vs 5 complex ones).
This problem can be solved by making uint256 much easier to use when coding in Cairo. Cairo 1.0 should be a big step forward in that regard. More details coming soon(ish)