Do you need inlining if you just use fixed monad transformers?

I am not sure what you mean by "fixed" monad transformers, if you mean writing your own newtype where the functor variable is the only type variable, essentially what you are doing is hand-inlining the monad transformer, and so no, if you inline by hand, then the compiler doesn't need to do it.

Haskell inlines all newtype definitions automatically, so if your monad transformer has all of the type variables bound (except for the functor variable, because that is a special case the Haskell compiler is specifically designed to handle) the compiler will usually reduce those to ordinary lambda expressions automatically, and lambda expressions usually optimize to the most efficient machine code.

The only time the compiler cannot reduce a newtype to an efficient lambda is if the non-functor variables, e.g. the state type variable or the exception type variable, are unbound. Those values could become anything at all at its call site, limited only by the constraints set by the type context. So the type context information, a lookup table of type class instances, must be associated with that lambda expression, and in order to do that, the compiler must create a closure around those values. Creating closures allocates values on the heap, and this is much, much slower than efficient lambda expressions, and no faster than allocating a data constructor as with Free Monads.

Alexis King did a presentation on it where she explains all of this extremely well, if you are interested: https://youtu.be/0jI-AlWEwYI

It is a bit long, but at 17:40 or so she starts talking about strategies for how monads and effects can be implemented in the GHC intermediate code, and compares Free Monads and effects to monad transformers. At 21:15 or so she begins to explain how newtype types can be optimized away completely, newtype constructors don't exist at all in the low-level code, they are a "zero-cost abstraction." On the other hand, data constructors (used for Free monads and effects) always allocate something on the heap which is an order of magnitude slower.

Then at around 27:45 she begins to show how newtypes with type variables cannot be inlined across module boundaries for the reason I explained above (type context tables associated with closures), and so monad transformers cannot be optimized across module boundaries.