But even in real life, you generally (generally, mind) have some idea as to your chance of pulling off some kind of feat such as an acrobatic maneuver or an attack. This is, after all, why you trained for years. If you're defending against the attack of some GM run foe, seeing his die rolls helps you measure his skill. This is a natural assessment which any skilled combatant (your players, right? They aren't running with the NPC Expert class, are they?) would be able to make after crossing blades with an opponent for even a few seconds.
And even if you're just dodging some kind of magical attack which you aren't familiar with, I don't find that seeing your dice results or the attackers dice results ruins the suspense in any way. It allows the players to attempt to measure their defenses against the attack. This is how most good novels are written, and that success lends itself to good RPG storytelling as well.
And in the final assessment, it promotes honest play. The players know that their GM isn't screwing them, and the GM knows that he is providing a good story without needing to resort to cheats.