Back to the original question of swords as opposed to cavalry...
I have always liked the whole tradition and good form of excercise aspect of the Imperial Marines being trained in cutlass. I also think the idea of having a good bladed weapon available for combat in a vacuum makes sense (I had not thought of the bayonet...cool idea!).
The thing I have always found odd is that the Imperial Marines are trained in what is primarily a slashing weapon. Sure it might tear great big holes in a vac suit, but I would think the slashing movement would be much less controllable in a zero-G environment than a thrusting movement like you would get from a rapier or other thrusting blade (bayonet!). Plus, if the vac suit is at all armored, a thrusting blade might have a better chance of penetrating. The puncture would not be as large and might be easily sealable, but you would not be as likely to loose control and would be in a better position to hit your opponent again or defend against another opponent.
I suppose there is no reason that tradition can't still be an explanation:
Marine Private: "Sarge, why the *beep* are we learning to use a cutlass? Its gonna send me flying if I ever take a swing at someone and the grav field's been cut."
Marine Seargent: "We aren't here to argue with thousands of years of tradition! We are here to learn how to fight with a Marine cutlass! ... However, I can't recall ever finding a regulation denying a marine from carrying a thrusting weapon as well as their cutlass..."
I've always assumed that the tradition originated with old Terran military tradition carried into the stars by the Terran military and then the Rule of Man and eventually to Third Imperium. That makes it an impressive tradition...it also provides a long time for it to have shifted towards a more practical weapon, like a heavy rapier. As for MTU, I've considered varying it by region or sector depending on the level of Solomani influence and so on.