I doubt that seriously. Could you write a complete Mars landing project in Haskell for instance? That would impress me. That's the area where Ada excels, or (less impressive) C and FramaC. But Haskell? No way.
AFAIK there is not one serious large project written in Haskell There is not even one sophisticated Haskell IDE for daily use written in Haskell (excuse me Leksah). Tell me if I am wrong, and if there actually are really big Haskell projects. Please don't listen compilers, they are not really complex.
The only advantage which Haskell actually has in comparison to other modern languages is its greatest disadvantage. The overall rock solid type safety of the whole application makes it very difficult to add additional unpredicted functionality which requires a significant change in many modules (where on the other hand the type system helps a lot). I am very impressed by the efforts and the implementations of Haskell but the simple fact that the Cabal hell -- for the simple job of a basic package manager -- lasted for years reveals that Haskell is not that practical after all.
I invested a lot of time to learn Haskell to use it seriously but after I switched to Nim (nim-lang.org) I realized how easy I can get real productivity.
Depending on what you mean by "in Haskell", probably. You can write hard-realtime software in an embedded DSL in Haskell that gives you explicit control over timings, scheduling, etc, while still giving you Haskell's higher order features for composing your programs.
https://hackage.haskell.org/package/atom
As I understand, the company that wrote it uses it in production in automotive systems.
What is an example of an extremely complex problem that you have solved that would be vastly more harder to implement in another language.
The most powerful thing that I have noticed is the type system. When you have a complex problem, you end up breaking it up by writing a lot of functions. In case of a language with a less powerful type system, it is hard for you to string them all together to build the complete program.
But with Haskell, if you have cared to actually annotate the types, this becomes a really trivial task. It also detects flaws in your reasoning (because the result of the previous step is incompatible with the input of the current step).
So, doing this would be vastly more difficult in a language like Python or even a language with less powerful type system like C.
As is the JVM (and most languages running on it). Not only that, but the JVM has actually a proven track record of being good and performant at it. And you can solve these problems with pretty much the language of your choice.
What makes you think Haskell is well suited for it? Immutability? This is available in a lot of languages (and for languages where it's not enforced, simple programmer discipline and code reviews address it).
On your second point, while it seems nice to have Haskell features slowly percolate into other languages, I urge caution in thinking that's a panacea for not learning more complex languages. Haskell is greater than the sum of all it's features. It's power comes from the combination of everything working together in a very well thought-out way.
So I don't necessarily disagree with your tone, just some additional commentary from someone who knows C++, Python, Java, and Haskell equally well (and perhaps equally bad ;) ).