That seems like a much minor situation compared to not being able to reverse map.
You could have a situation where you have a string as a code, and then the display name for example, and you can't really do that as is now. This seems more useful than checking for the type (which in a numeric enum is either a number or string, so you would still need to do some work to properly validate it).
If you want to have the reverse map, you can trivially build it yourself. But if the reverse map did exist (rather, if the map started off as bidirectional, which is the only option on the table), it'd be impossible to properly construct the one-way map.
You mean because of using the same string for a key/value? I guess I see the potential problem.
Anyway just think that it might be a bit confusing to have the enum work slightly different depending on whether its using numbers or strings. It can caught some people off guard.
You could have a situation where you have a string as a code, and then the display name for example, and you can't really do that as is now. This seems more useful than checking for the type (which in a numeric enum is either a number or string, so you would still need to do some work to properly validate it).