How effective the shoving approach is depends on the target's AC. Against low-AC targets, making two melee attacks is the better option. Shoving the high-AC target prone kind of debuffs it. The tactic is not as effective against every target (either by RAW or by my suggestion).
It makes knocking many targets prone the preferred go-to, as opposed to situational. Knocking a target prone already has some good uses (mob tactics etc.), just doesn't seem to be necessary as the go-to tactic against high AC opponents.
Also, it makes the BM trip attack and the shield master ability even more effective than it already is - there are ripple effects.
On the other hand, if an approach works against a target, if it was just making the ordinary melee attack, why would it not be used every turn?
I don't understand the question?