Installation will no doubt be more expensive in the US, but there is no reason for AC itself to be (if anything, most kinds of hardware seem to generally be cheaper in US than in Europe).
I suppose it's hard to complain too much. HVAC installers need to have some decent technical background, troubleshooting skills, and their bodies tend to get injured/broken by the time they're in their late 40s like most manual labor trades. A HVAC installer/tech can make $80K or more a year, which makes it one of the few jobs still out there where you can make a decent middle class income without tons of schooling.
Installing a mini split is nowhere the difficulty of an HVAC though, assuming your have the electrical circuit (which I'd guess would be an electrician's job not HVAC) it's a few hours' work, at least for a simple case and if the installer knows what they're doing: pierce the wall, mount the external unit, mount the internal unit, connect the two, charge[0], done.
By "simple" I mean a 1:1 setup with both units mounted on the same wall (and a wall-mounted indoor unit). Obviously a more complicated setup (multi-zone, slim duct, more distance between the two units) would take more time and be more expensive.
I can see $2000 for a non-trivial multi-zone setup.
[0] if you're handy there are mini-splits sold specifically for DIY installations which come pre-charged, though that means the pipes won't exactly fit the distance I guess
In addition, running the electrical is usually done by the HVAC company and setting up the mounting pad for the outdoor unit.
I completely agree that it isn't rocket science, and it's well within the realm of a skilled DIYer with about $250 in specialized tools. However, I can see why an HVAC company charges as much as they do. For an average install (not dead simple), it's probably 5-6 hours of labor, they have to pay for the company equipment, vehicles, health insurance, permits (my township requires one for a mini), taxes, etc.