Because, as you point out, credit cards have large transaction fees. This is an inevitable consequence of it being a "pull" payment mechanism.

If you want to fix the paying-rent problem, you need to convince US banks to provide an efficient "push" mechanism for payments such as exists in the rest of the world -- i.e., a way that you can tell your bank "send $X to account number 12345 at bank number 6789".

Do other countries have regulations that prevent banks from charging large sums for wire transfers?