This would require you to add MPTCs to the language standard, which means standardizing how they work.
Any solution involving SomeException or any of its variants is going to drag in GADTs, Typeable, higher rank types.
... and it would drag them inexorably into the Prelude, not just base.
Compared to a simple
class Monad m => MonadFail m where
fail :: String -> m a
that is a very hard sell!
On the other hand, I do think what we could do is add more information about pattern match failures by adding another member to the class
class Monad m => MonadFail m where
patternMatchFailure :: Location -> String -> whatever else you like -> m a
patternMatchFailure l s ... = fail (code to generate the string we generate in the compiler using just the parts we're passed)
fail :: String -> m a
Then the existing 'fail' desugaring could be done in terms of this additional member and its default implementation.
This remains entirely in the "small" subset of Haskell that is well behaved. It doesn't change if we go and radically redefine the way the exception hierarchy works, and it doesn't require a ton of standardization effort.
Now if we want to make the fail instance for IO or other MonadThrow instances package up the patternMatchFailure and throw it in an exception we have the freedom, but we're avoid locking ourselves in to actually trying to figure out how to standardize all of the particulars of the exception machinery into the language standard.
-Edward