I still feel like there is an important point you're walking past.

If there are 2^16 different combinations that are relevant, then you still need to handle these 2^16 combinations in your code. If you're ready a configuration file from a user and only different subsets of them are valid, somewhere in your code you still need all of the complexity to let the user know they have passed in an invalid combination. And all of that logic is equally or more complex than an enum.

If all of those cases can be handled by a few simple "if" in your code, then you'll have only a few valid options in your enum. If you have a ton of valid options you need to list in your enum, then you'll have a tone of cases you need to handle in your code.

Your underlying complaint to me sounds like you've received a lot of complex cases via your requirements. But either way the complexity is there in your code regardless of whether you validate it upfront in an enum, or deep in our code base.