As has been stated at numerous WTCs, in forums, etc., it is an extraordinarily bad idea to change the style of Input and Output. This has been the case since at least Mathematica 6, if not earlier.
I frequently edit the default style sheet (I hate Arial), but after noticing the unintended consequences of editing the styles of Input and Output, let alone StandardForm, I leave them alone.
I have not tried Bruce Miller's suggestion, but apparently, this has undesirable side effects as well.
I have not even thought about issues with non-roman typefaces.