In fact, a good overload would not lose functionality on normal arguments. For instance, what if someone wanted to instrument logging by absolute filename, to collect statistics? Extending -e to do this would be easier than replacing every file test operator call everywhere, including external packages.
For these kinds of questions, it's better if we get a real sense of the OP's ultimate goal and purpose, before declaring "that's a bad idea" just because it usually is.
Quantum Mechanics: The dreams stuff is made of