That's completely false. They work just fine despite not being terribly efficient at least provided you install them correctly (but that caveat naturally applies to any window unit).
In fact despite the low efficiency using only one in a single room is likely far cheaper than cooling the entire house. It's the same principle as an electric space heater versus a whole home heat pump.
Of course running a minisplit only in the one room would be substantially better but for a 1 kW unit the difference is less than $1 per day (unless you're subject to the California electric grid I guess).
Since these one tube systems just push hot air out, you are creating low pressure in your room and you will suck the air in from somewhere. Often times simply from outside from the leaky windows.
I don't understand why it's hard to buy systems with two hoses that would keep the pressure in the room.
As to the negative pressure, personally I just leave the door to the room cracked open very slightly. But if you have central heat ducts air will get sucked in through that no problem.
In system where the pressure would be equalized the leaks would be much smaller. For some reason it's impossible to buy these type units in EU.
That’s way high: You can buy 2 for that much if you want a big name brand that provides support for self-installs. 3-4 of them for $5k if you don’t care about that…
Source: I’ve done it