After a lot of Google and asking professors about the two quantization methods, I have learned that first quantization is what you use to quantize classical particles, while second quantization is what you use to quantize classical fields or a large number of classical particles.
If, according to QFT, every particle is an excitation of a field, then why does the first quantization method work for some particles? Is it an approximation that works because the wavelengths involved are much smaller for, say, an electron than a photon?
If that's not the right question because I'm wrongly assuming that you shouldn't be able to use 1st quantization for fields, then why can't you use it for the electromagnetic field? I mean, you can to an extent, but it feels forced, the whole reason being Gauss' law forbidding a position eigenstate, but why does something similar not happen for other particles' fields?
I'm interested in why the localization problem applies to the photon and not to, say, the electron: Why can you (in principle) exactly locate an electron in space, if you can't do it for the photon? They are both fields, shouldn't they follow similar rules? Obviously they don't, so what is the difference?