What is the benefit of Shoving someone 5ft (eg Tavern Brawler)?  Am I missing something?  Does that move them 10 ft in total from you so you can avoid an Opportunity Attack?

Other than if they are near a cliff or near some ongoing spell that will cause them damage if they shoved into, I don't see the benefit?

For most foes, with a reach of 5 feet, yes, shoving them 5 feet away from you will allow you to withdraw without eating an Opportunity Attack.

And, yes, it's useful for pushing foes into ongoing hazards. Unlike many other ways for an unarmed fighter to move foes, there's no Saving Throw required. And it works on any creature hit, regardless of Size (Unlike the Push Weapon Mastery, which only works up to Large size)

And then there's this bit under "Moving Around Other Creatures" in the Combat / Movement and Position section.

You can’t willingly end a move in a space occupied by another creature. If you somehow end a turn in a space with another creature, you have the Prone condition (see the Rules Glossary) unless you are Tiny or are of a larger size than the other creature.

So if you move one creature so that it shares a square with another creature, and both of them are larger than Tiny, at least one of them will be Prone at the end of your Turn. How advantageous or disadvantageous that is will depend on the positioning of the rest of your party, but at the very least, it means the Proned creature will have to spend half its move on its turn standing back up if it wants to end the Condition.

You already list a lot of the benefits. Battlefield control powers are as useful as the player makes them. 

Shoving creature A into creature B does not cause them to go prone. Read the rule again and you'll see that they can't willingly share a space with another creature after ending a move on their turn (not yours). Their "move" occurs on their turn, shoving them doesn't count as their move, and don't forget the rule even uses the word "willingly". Shoving them does not count as them choosing to move. If you shove them so they share a space, and if on their turn they do nothing to move out of that shared space, THEN they go prone - not at the end of your turn, its at the end of their turn.

Shoving does have many advantages. If you get multiple attacks, you can use one to shove, still allowing you to take at least one damaging attack, then move away without having to disengage. This is especially useful if the enemy has the Sentinel Feat, which would be triggered if you disengaged. You can also shove to move an opponent away from an ally, allowing them more breathing room (or to escape an aura effect). Don't forget you can also shove friends. Another useful tactic is to shove a monster (that entered your room) back into the doorway, then move up to block them. This keeps enemies who have yet to move into the room from being able to do so. Now you can fight them one at a time. Shoving someone can also be used to knock them prone, allowing others to possibly get advantage against them.