> But it isn't? For e.g. outside sheds (heated to 7°C) the COP can theoretically go up to 27. For solar panels, the highest theoretical efficiency is well below 100% and the bound isn't communicated.
That's just another way of saying that framing it as efficiency and disregarding that you're moving heat from a colder reservoir is incredibly misleading. Now the marketing department can put a giant "1300% efficient*" sticker on the dual use heat pump even though it's worse for heating to 24C. A heat pump is fundamentally moving heat. It's in the name. (Heat created + heat moved) / work in does not map to an intuitive or technical notion of efficiency, and framing it that way is encouraging a mental model which is not just quantitatively off, but fundamentally wrong. It's also a distinction that is subtle enough that it is very hard to see while you are confused. This is the almost worst kind communication failure (maybe just after using a dimensionless number for insulation, or using kilo for kibi) because it's so hard to correct. It leaks into other domains and destroys communication, allowing marketers to lie, and requiring a constant treadmill of new terms to fix.
> For solar panels, the highest theoretical efficiency is well below 100% and the bound isn't communicated.
The absolute bound is carnot efficiency, which is about 80% for coupling to the sun. This is close enough that out/in is fine. Additionally out/in is the correct model because you are converting energy not movng it. 'Simple silicon cells can't exceed about 35% efficiency because they need to pick whether to waste energy in blue light or ignore energy in infrared' is the only other piece of information needed to convert that to a quantitatively and physically complete model. You can even communicate it succinctly by drawing a rectangle on a black body diagram.
> saying in school maths that you can't take the square root of -1.
This is also anti-education and a far worse sin because it is crushing one of the few moments where mathematics might actually be learned in a maths class instead of rote algorithm memorization. A teacher should never ever say this. Far better to say something along the lines of "that's a question that doesn't have an answer when we're talking about numbers on the number line, come talk to me about it later". Or "it's really cool that you're thinking about that, here's the khan academy and wiki pages, write a letter telling me all about it instead of your normal homework". Or even "think about it and tell me what you think the answer should be".