This sort of assumes that the objective of a language should be to create "an awesome IDE experience", while there's a good chunk of people who think having to have an IDE is simply a flaw in a language.
Coming from the other side, it seems like "because you should be able to do it manually" seems like a poor reason to not provide the option to have things automated.
The computer is more accurate and faster at determining the type of an expression than humans are. That seems like a big part of the value proposition of static languages. So why not let it tell you the type in the editor instead of having to stop what you are doing to compile it (which may require fiddling with the code to get a meaningful type error)?
So you mean, Haskell has a bunch of people who prefer to use the force rather than their targeting computers? So Haskell's language design obviates the need for good code completion or pervasive display of type inference results?
Also, as the joke goes, well typed programs can't go wrong in Haskell because the debugger just isn't that great.
Most serious Haskell users are most likely using a REPL and when doing this it's trivial to get and think about type information even while checking other stuff. It's also obviously part of the thought process while developing anyway, so I don't see the same value in this as you do. There's a cost to having a full IDE anyway and it's more sensible to get the features you do want (auto-completion, etc.) from plugins and then not using a IDE.
Even if you want these things, there are better ways to go about this instead of making a whole gargantuan interface to get a couple of features.
I'm not usually one to tell people what they should be working on, but time could be spent on this instead:
The computer is more accurate and faster at determining the type of an expression than humans are. That seems like a big part of the value proposition of static languages. So why not let it tell you the type in the editor instead of having to stop what you are doing to compile it (which may require fiddling with the code to get a meaningful type error)?