Shove is an awesome strategic Action in 5e.

Shove that is a Bonus Action that sends people flying more than 5 feet/1 meter is broken.

Save some room for special abilities and feats, Larian. Don't make it so everyone can shove as a bonus and more than 5 feet. There are feats that can increase this ability, making feats more important and desirable.

Same goes for Throw. Tame down the throw mechanics for everyone. Then create feats that a person can take to increase your throw potential.