One thing I've learned from my 30-odd years in the electronics/computing industry is that we tend to do things because we've always done them
I've also discovered that even after 30 years I can do reasonable work without fully understanding a lot of what I do. I don't understand, for example, how we can get megabits per second data transfer down a twisted pair of wires, when I've seen very thorough theoretical analysis that proves that this is impossible. None of that stops me using the Internet, however.
I'm aware that AC currents can be carried in space, and that this gets easier as frequencies increase. After all, a simple capacitor is a great insulator at DC, having no conductive path. How current gets from one limb of a dipole to the other is non-straightforward (at least to me), but you can use Maxwell's field equations to show that this happens, and even predict the impedance, etc -- in simple cases. I strongly suspect that anything more complicated than an ideal dipole is impossible to handle using purely theoretical techniques, and we need computer modelling and such-like. My feeling is that if there _were_ manageable theoretical interpretations of real antenna configurations, there would not be so much uncertainty in this subject area.
Whatever happens at AC, however, the inescapable fact is that our transmitters are powered at DC. With a battery, there's no way to take more current out of one terminal than you put back in the other, not even for an instant. That means that no current can "leave" the antenna, unless an equal and opposite current re-enters the equipment from somewhere. And that in turn means that no common-mode current can flow down the feedline, away from the source, unless there is some way for it to return. That way might be through electromagnetic coupling -- there need not be a DC current path -- but it has to exist somewhere, somehow. If it doesn't, you end up with the impossibility of unbalanced _DC_ currents in the supply.
It may be that using coax to feed a dipole makes common-mode problems worse than using a balanced feeder; but I'm not at all convinced that describing the coax as "unbalanced" is an explanation for this. There has to be more going on; I just don't understand what it is.