They all are focused too much on optimizing damage. There isn’t enough difference to matter at the table, just play what you want. I typically pick a style to match the mini I am using for that PC.
Inspiring leader is one the best feats in the game, maybe the best feat.
Heavy Armor Master plays a lot better than it sounds. For a VHuman I take it almost every time at first level to get most mileage. Think about how many times you get attacked wherein the feat comes into play, you might get attacked 3-400 times before 5th level as you will be the frontline. It would be worth it if you only got attacked 100 times.
Warcaster is good even without BB if you use Command and have another PC that does same or uses Dissonant Whispers or other fear affects to make them move. You just want as many chances as possible to roll a crit especially if you can tack on a doubled smite.
The reason I use Shield Master a lot on a Paladins is that increased chance to land that doubled smite. It’s more effective in our game since critical hits for us is max weapon damage + the extra crit dice so as not to get a crit and then crap out.
Inspiring Leader is OK but HP is an inefficient line of defense unless you've got resistance. If you've got say a Barbarian and the DM is giving you plentiful short rests it's not a bad pick to increase your dungeoncrawling mode sustain, but you'd rather see it on a Sorcerer or Bard than on the MAD as hell Paladin.
Heavy Armor Master only factors in when you actually take damage, and even then the true impact comes down to how many times you took damage
during a fight, as it's generally trivial to patch yourself up between encounters. It kicks ass when 3 bps is like 25 to 10% of your HP applied per instance, but once you're past level 4 you should be really be thinking about how many times per fight it's actually applying. Absolutely worthwhile if you have an odd STR score you need evening out, but that's only going to happen with rolling, and from an optimization perspective PAM does far more for you at early levels.
You're a little confused about War Caster: the feat lets you cast spells as a reaction in situations where the enemy would already provoke an opportunity attack, so you pair it with Booming Blade so you can cast that in lieu of making a normal attack.
You can replace one of your Attack action attacks with a Shove attempt, so if what you're looking is crit-fishing then PAM is identical in function since you get a shove plus two attacks on top. Shield Master is nice for different reasons (namely, reaction evasion to avoid chip damage), not as an offensive tool.
5e has a narrow window for optimization - there aren't really that many picks that make a difference - but the ceiling is high. For example, take two level 5 Paladins: one is a VHuman who started with 16 STR, took Polearm Master and Resilient(CON). The other is a Tiefling who took HAM at 4 to round up his CON to 16, and wants to be the tank so grabbed Protection Fighting Style.
Do you want to know how much more damage the optimized human does? +108% on a typical fight. Literally two tieflings worth of DPR contribution, and if you put them together in a party and they played at equivalent skill levels, it'd be easy to tell who is the greatest asset to the team - because being a little individually tougher does not help the group overcome challenges as much as being twice as good at inflicting The Best CC.
I agree with the sentiment of playing what you want, and there are many ways to contribute to the cooperative challenge-solving game that is D&D besides damage numbers, but to say individual character-building choices within a class don't make much of a difference is being disingenuous.
and second- it's too late, dices has been thrown 
