I'm not sure if it's been done in any other games, but why not different weights for classes? I know that in R6V you could wear no armor to move faster, and the more you put on the slower you went, but I haven't seen anything like that in games I've played since then... and that was 2006.
For instance, Support would have extra armor, but would move a bit slower, and make more noise as they moved. Recon would have very little armor, but would move quickly, and be relatively silent while sprinting. As for assault, it's right in the middle -- average speed, average volume, average armor. I don't think this is a very innovative idea, and I'm surprised it hasn't been implemented. Or hey, maybe it has been and I just haven't heard anything about it then. I think it would make the gameplay more interesting, and make people more likely to change up classes rather than picking one and sticking with it.
In Brink you had 3 weight classes, small, medium and heavy. In that game the bigger your weight the bigger a target you were, the more health you had, but you could only do basic parkour moves, whereas the lighter you were, the smaller and faster you became and you could parkour more, but you had very little health.
I like the idea