Here are two that lack a Button 9 that I have at hand:
Those are officially-licensed, but I also have a couple of Chinese clones which skip Button 9, which I assume is what your code is looking for. There are also SNES-inspired controllers that might not map select to Button 9. Yes, Backspace with a controller just switches to keyboard mode, it doesn't clear the button binding.
By suggesting that you might use another button, you're still making some assumptions about what the button layout and mapping of the user's controller will be, and arbitrarily choosing a button that will be gated off. It would be better to have a universal key (such as Backspace) that will clear a button binding or a keyboard binding, and that all PCs are guaranteed to have.
The other option would be to overwrite an existing bind, possibly with the red text prompting for a second confirmation press, instead of simply refusing to remap.
For the record, local co-op and such is still a completely legitimate reason to have multiple controllers connected to a PC. Also, some disability controller setups might still use multiple controllers, although I don't expect indie games to support those out of the gate.
EDIT: Wrong pic for the Gen/MD controller, fixed. Also, I realize that historically, indie games' solution to controllers has been "just use Joy2Key", so I appreciate that you are actually supporting controllers. My suggestions are only intended as constructive criticism.
EDIT 2: Tried a couple of generic PSX controllers of different make/model, which have "Select" mapped to Button 9, and it still doesn't clear the binding. I've tried all of the buttons (including thumbsticks) on both, and none of them do. I'm not sure which button you're looking for in the code to clear the binding, but it doesn't appear to be working.