Why is it so expensive? It's like $1k in Finland.
You can definitely do it for cheaper. There are $1000-$3000 single-head units available online for self-install, and you could hire an HVAC person to come out and do the high pressure line part of it (or all of it) for a similar range. It just gets expensive with the name-brand ones. For some reason that $2k-6k turns into 10k-20k when you switch to a name brand (e.g. mitsubishi). They're only available through specific installers, and using a non-authorized installer means your warranty is void.
Of course, a multi-room install would probably get expensive quickly here too.
[1]: https://kaiteki.no/