Light can't have mass because relativity says that to accelerate any amount of mass to the speed of light would require an infinite amount of energy
yes, but this has been only confirmed by very brute-force measurements.
say for instance the ultimate limit was minutely beyond that of light, light could therefore theoretically still have mass, but it would be so hard to detect when not moving (relatively) that we wouldnt be able to observe it.
the "light moves fast as light" idea is redundant, the point in question here is if light would be the absolute limit.
whats especially important about this is that if the mass is small enough the particle would take on the dual properties of light that we currently see (we already see this sort of mass-energy duality in electrons, which are mighty small)
you have to understand, I'm not proposing any new theory, I just want to find out why.
Have you read "A Brief History of Time" by Stephen Hawking? I can't remember if that topic is explicitly addressed in there but that is a great book for discussions of that kind of physics.
I'll check it out, thanks