Why can't an interface implementation return a more specific type?

Usually, I'd say that it would be a case of balancing the benefit against the added complexity of supporting such a feature. (All features take effort to design, document, implement, test, and then developers need to be educated about them too.) Note that there could be some significant complexities if you wanted to support returning a value type which implemented an interface, for example (as that ends up in a different representation, rather than just a reference).

In this case, I don't believe the CLR even supports such a feature, which would make it very hard for C# to do so cleanly.

I agree it would be a useful feature, but I suspect it hasn't been deemed useful enough to warrant the extra work required.

The feature you're asking about is called "return type covariance". As noted on Wikipedia, Java and C++ both have it, which perhaps makes it surprising that C# does not.

Eric Lippert confirms in the comments on this answer that this feature wasn't implemented because it wasn't deemed worth the implementation effort. (A previous revision of this answer assigned responsibility for that decision to Eric personally; he says that this is incorrect, and that if any one person is responsible it was Anders Hejlsberg.)

Regardless, there are now various proposals to add it to the language (see https://github.com/dotnet/roslyn/issues/357, https://github.com/dotnet/csharplang/blob/master/proposals/covariant-returns.md, https://github.com/kingces95/coreclr/issues/2), so perhaps it will get implemented in the next couple of years. Per those discussions, it doesn't sound like there are any profound reasons why the feature shouldn't exist in C# in principle - rather, it's just never so far been judged worth anyone's effort to implement.