> It's not out of thin air, it's from a very empirically successful theory: Maxwell's electrodynamics.
That was the source of the assumption, yes--as you point out, Einstein said so in his original paper. But from the standpoint of mechanics, as opposed to electrodynamics, it was pulled out of thin air. There was no reason based on mechanics to make any such assumption. In fact, everyone else except Einstein that was working on the problem was looking at ways to modify electrodynamics, not mechanics--in other words, to come up with a theory of electrodynamics that was Galilean invariant, rather than to come up with a theory of mechanics that was Lorentz invariant.
> you either abandon the idea that laws of physics remaining the same under all reference frames, OR abandon Galilean velocity addition
Or, as above, you look for a Galilean invariant theory of electrodynamics. Of course we know today that that is a dead end, but that wasn't known then.
That was the source of the assumption, yes--as you point out, Einstein said so in his original paper. But from the standpoint of mechanics, as opposed to electrodynamics, it was pulled out of thin air. There was no reason based on mechanics to make any such assumption. In fact, everyone else except Einstein that was working on the problem was looking at ways to modify electrodynamics, not mechanics--in other words, to come up with a theory of electrodynamics that was Galilean invariant, rather than to come up with a theory of mechanics that was Lorentz invariant.
> you either abandon the idea that laws of physics remaining the same under all reference frames, OR abandon Galilean velocity addition
Or, as above, you look for a Galilean invariant theory of electrodynamics. Of course we know today that that is a dead end, but that wasn't known then.