Recently I came across this question on this site, where the answer written by @AndrewSteane says (paraphrased for convenience)
The electromagnetic interactions between two particles can be expressed as an integral over all the ways in which one object interacts with the electromagnetic field which in turn can interact with the other object. These interactions can be expressed in a number of ways, but a particularly nice way is to assert that an electron emits something called a virtual photon. This virtual photon is different from a real photon in that it should not be considered as a thing which could in any sense go on its way to the rest of the world and interact with anything else. Rather it is a way of talking about part of the interaction between the particular two electrons under consideration.
And hence my question: If they aren't even real photons, why did we call them, well, photons? And then why is the quantisation of all the $4$ forces taken so seriously when it is just for mathematical elegance and nothing else?