Technically you’re correct, a 12000 BTU minisplit only uses around 1000 watts while running which is just over 4A.
The breaker size being 20A 2P is a consequence of the NEC requiring you to size the wire based off the equipment nameplate rating of 15A, which is based off the full load amps of the motors inside the equipment.
Full load amps is the max amount of current a motor can draw at a specific voltage and is used for sizing wire and overcurrent protection for a piece of equipment. It doesn’t always match up the current a motor draws while it’s running normally. You take full load amps times 1.25 to get minimum circuit ampacity, which you use to size the conductors.
So while you are correct that a 240V 12000 BTU minisplit wont draw anywhere near 20A, the specific minisplit I looked at required a 20A breaker due to the minimum circuit ampacity being 15A. If the MCA was 12A, you could use a 15A breaker; an MCA of 8A would allow using a 10A breaker, and so on.
If you use fuses, you can size the overcurrent protection at 100%, breakers require 125% of the load for a continuous load. So you could use a 30A fusible disconnect switch fused at 15A for a unit with an MCA of 15A.