I have read over a dozen questions about the speed of light -- "why it $c$ constant?", "why can't anything travel faster than light?", "how do we know this?"
The responses are quite clear:
The invariance of light speed is determined empirically (e.g. from the Michelson-Morley experiment).
The speed of light is simply an axiom for physics and was discovered experimentally.
The invariant value of $c$ is a fundamental property of the universe.
My question is why can't the invariance of $c$ not be deduced theoretically with the following logic.
As an object's velocity increases, its kinetic energy also increases.
The kinetic energy growth is asymptotic, meaning it approaches infinity as the velocity approaches some value.
This makes it impossible for anything with a mass to reach this velocity because it would require infinite kinetic energy.
Therefore velocity must be have a limit.
See, this makes much more sense to me than the claim that the invariance of $c$ is just a postulate from lab work and that there's no reason for it to be invariant other than "it's just the way things are".
I suspect I've made a mistake. Perhaps the idea that an object's mass increases rapidly as speed increases comes from special relativity itself, which is derived from the assumption that $c$ is invariant. This doesn't, however, seem obvious to me since we should be able to observe this effect in experiments.