The Signal messenger and protocol.

What is the use case for it?

The same use case as any crypto - to use as currency and pay debts.

Seems kind of pointless and a lot more tedious than just a bank transfer.

The same can be said of every crypto which doesn't hit any kind of adoption.

Why does signal include crypto nonsense in their app (I like crypto, but just can’t see any reason why it should be integrated in the app)

It aligns with Signal's mission statement to "Protect free expression and enable secure global communication through open source privacy technology." [1]. The reason it was integrated into the app was to support crypto that was "easy to use". The same way cash provides privacy by not allowing third parties to see what you're doing, they believe(d) that enabling a privacy preserving crypto wallet would further "protect free expression".

I’m sad that signal does not have support for 3rd party open source clients that could remove such features.

It's not not enabled by default and makes up for (based on github commits and pulling a random number out of my ass based on my continue following of Signal's development) less than 1% of development work since it was introduced.

Why not add support for monero instead?

Monero did not meet the technical requirements that the Signal developers were looking for at the time. Signal has commented that they would consider adding other crypto, as long as it meets the technical requirements - which I don't have so can't source unfortunately.

[1] https://signalfoundation.org/en/