Underpromotion

 Excuse me being a novice. But in certain situations (see diagram) would it not be advantageuos to underpromote, hoping that this underpromotion would convince your opponent that an exchange is not worth it?

For example, if I were to promote to a queen here, I would be quickly consumed by my opponent's queen. However, if I chose to to underpromote to, say, a rook, perhaps I could convince black to ignore the promotion; leaving me with slightly more leverage.

Comments?

There are times when underpromotion makes sense, but never for the reason you've given. Underpromoting so as to be "not worth it" implies there the opponent has a better move (than the capture) to be made elsewhere... in which case you should have promoted to Queen so as to prevent the enemy from having that better move available.

In the first diagram, you are just giving black the benefit of choice.  Black can either trade off the rook anyways (leaving him with the same position had he traded off a queen), or he can avoid the trade and be left with more material.

The point of underpromotion isn't "Leverage".  If its not to attack where queens cannot (in the case of knights), its to avoid stalemate.  E.G, in the famous endgame study about the saavedra position.

Saavadra however found a great way to force a win.