Shield Master
bonus action shoves, add shield AC to personal Dex saves, use reaction to negate half damage on Dex saves
Design: Fairly okay. I find the AC save bonus needlessly constrained to effects that target only you. Also, it's a bit weird how this becomes (much) better with a +3 shield (which already is over the top). This could have being phrased either as you gaining advantage, or a +2 bonus that applies to all dex saves you make.
Fun: Bashing your enemy prone is a great way to embarrass it
Power: Bonus action shoves isn't as valuable as bonus action attacks (which can be used to shove); The AC save bonus isn't generously worded. Still, I hesitate lowering this into purple.
I feel as though I want to mount an impassioned defense of the Shield Master feat, which is a bit awkward, as you haven't really been unkind to it. I guess I think that it deserves a bit more appreciation than you have shown it. So here is my paean to the Shield Master feat.
I'm currently 10 levels into playing a sword & board battle master. He's got the Heavy Armor Master and Shield Master feats, and so far, I would have to say that both feats have served me well, Shield Master in particular.
As you pointed out, the shield bash is fun, and in my experience it works more often than it doesn't, so it's also effective. The party is melee heavy, so the effectiveness of putting an adversary on its back in the middle of the scrum is greater than it might be if half my companions were hiding in the tree line. So I suppose my high opinion of the feat may be somewhat colored by circumstance.
The most obvious impact has been on my fighter's action economy. I picked up Shield Master at 6th and I'm now most of the way through 10th, so the character has had 1 Extra Attack in that time, and Shield Master has increased his attacks in a typical round by 50%. That's a lot. It sure feels like a lot. But that's probably not why I love the feat.
When you discussed the Mobile feet, you identified it as an enabling feet rather than a power enhancing feet. The same can be said for Shield Master. The Shove, after all, does no direct damage to the target. But tactically, it can put the target in a sharply inferior position, depending on the whims of the Initiative order and the state of play on the grid. And it's a tactical tool that can be brought into play almost every round. For a battle master, it also a tactical tool that consumes no superiority dice.
Here's a scenario that highlights the efficacy of Shield Master: At the start of my turn, I engage a target with a shield bash to the face, and put him on his back. Then I walk away, drawing an opportunity attack at disadvantage. When that misses, which it's likely to do, I hit him with a Riposte, saying to my DM,
"Je riposte contre votre monstre avec disadvantage." Then, engaging my second target, I
start my attack action. I've already had a profitable round, and now I'm just starting my attacks. And I'm a fighter. If this is round one then more often than not I've got an action surge in my pocket. If all my Christmases have come at once, I might be able to tag two more targets with Menacing attack before my round is done. Then I can turn to my fellow players and assure them that they all have nice characters too.
I think it's the enabling type of feats that I find most attractive. I like a feat that increases my degrees of freedom, a feat that can be tactically deployed in different ways depending on circumstance, a feat that gives me choices to make and results to rue or celebrate. Shield Master fits that bill, at least so far.
As the campaign continues, Shield Master will become less effective as the incidence of huge sized adversaries increases, just as the wizard's controller spells become less effective as legendary resistance becomes more common. And, starting at 11th level, I'll have another Extra Attack. Shield Master's bonus attack will recede in prominence. So far, I've only experienced the sweet spot. But it has been sweet.
And, yes, the boost to a Dexterity save situation that never actually comes up is worthless. They should not have included it. But this was obvious at the feat's first reading, and therefore did not color my expectations of the feat's utility. The gentle rebuke that WotC deserves for this should really just be a footnote. The bonus action is the thing.