Tripping can be pretty damn effective if used correctly and when we can get past level 4. If you know your other melee characters will get a turn before the enemy does, then tripping is fantastic. Additionally, if it's the first thing you do as a level 5 fighter, then your next attack will also be at advantage.
The problem is that it's still usually more effective damage-wise to make N attacks at normal than make N-1 attacks at advantage. Barring any crit shenanigans (Brutal Critical, Smiting on crits, etc), the math doesn't favor tripping until you can make ~4-5+ attacks on the prone character. The math is slightly better when you're turning disadvantage into normal attacking, but not by much
unless doing so then allows for a rogue to get sneak attack.
And of course, you have to take into account the chances that your Shove Prone attempt fails, in which case now you're still making N-1 attacks at normal.
