Anything can be used as an improvised weapon.
With those feats you can shove or grapple as a bonus action, but you only get one bonus action per round. You would have to use a special attack option (the ones with no damage) to make one trigger the other. I believe that could run counter to what you are attempting to accomplish.
By the time you get both of these feats, you could have two attacks per round and perform the "pin" without them.
Agh, forgot about that. Both feats are useful nevertheless, for instance i can grapple freely in first round, and shield bash after that. Surely i can use one of my attacks for shove/grapple and use bonus action for other. Then i would miss some potential damage.
Compare:
With both feats:
R1: bonus grapple, 1-2 normal attacks (grapple first as it prevents enemy getting up after shove)
R2: bonus shove, 1-2 advantage attacks
Rx: keep repeating either round for situation, new targets may be needed to grapple.
Shield master feat only:
R1: bonus shove, 1grapple, 0-1 advantage attacks
R2: bonus shove, 1-2 advantage attacks
Rx: keep repeating either round for situation, new tqrgets may be needed to grapple.
(Amount of attacks are in range and indicate if you are under or over level 5)
Thoughts on tavern brawler worthiness, constructive criticism and the like is welcome though.