Just to be clear - not all inverter aircons have this feature, it’s not required, but it does help in some scenarios.
I think most of the difference is made up by the explanation in the last paragraph about power factor.
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Then, since residential consumers don’t pay for bad power factor, we’re probably still at the same answer: The difference in actual consumed energy won’t be all that big.
Perhaps my explanation was not clear enough. The fact that the range in which the PF can vary is not really proportional to the work that the pump does means that when it is not doing any work, it still draws at least 50% of the real power it is rated at. So when loaded at say 70%, the inverter will draw less real power than a non-inverter.
Another thing I just thought about: single phase induction motors of this size (700-2000W) is usually only about 70% efficient. I don’t know what that figure is for the BLDC motor plus inverter, but I would guess it’s higher.
OK, still a bit confused about how power factor relates to this (apparent power vs real power), but I think I get the gist of it.
Your second point is also spot on, I forgot about that completely. Even if they are using a 3-phase AC motor driven by a FVD, you should see an efficiency improvement. The inverter itself probably has its own loss of around 8% to 10% I would imagine, but a 3 phase motor is apparently at least 90% efficient, so there will be overall gain that’s probably worth it.