While I like the idea/theory of being able to throw other frame abilities around to other frames, I haven't done it simply because I like how each frame is played with the abilities they have.
In all honesty, I would love to pick the abilities to move and swap but it should come at a cost, and a steep one at that. Either +20% cost to cast, -10% to 25% damage, -10% to 20% duration, -5% to 25% range or a combination of them rolled at random.
Right now I am totally in love with my Protea. I love being able to play "engineer" and supply ammo and shield buffs. The temp turret is a very nice flavor for the frame. The only ability I would swap out would be Temporal Anchor. As fun as the ability is, I find myself accidentally activating it more than I want to admit. Sometimes not even realizing that I did it until everything is moving in reverse!
I would be totally down for some ability swaps, but like I said. It should come at a pretty hefty cost that you have no control over.