I know next to nothing about physics, but isn't the "It just so happens" part of what you said potentially misleading? Isn't it that light is massless, so that directly implies that it would travel at the maximum speed?
It's a distinction with no difference. Only massless particles can move at the "maximum speed", in our Universe these are photons and gluons. And maybe gravitons, if they exist.
Similarly, massless particles can't move below the "maximum speed", as they'll have no energy or momentum and won't be able to interact with anything.
Why would the absence of mass force something to travel at the maximum speed? I could understand it being able to travel at that speed; why would it always do so though?
Theoretically, a massless particle can move slower than light. But then it'll have zero energy and momentum, so it won't be able to interact with anything.