FrogReaver
The most respectful and polite poster ever
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.
I consider a "loss" to occur when a character in the party dies. You can't die in combat if you don't hit 0 hp and inspiring leader really helps keep that from happening especially for the squishiest backline characters.
Also, if you're using a one handed weapon all it takes is a single level of hexblade to solve the mad issue.
Honestly, I think inspiring leader is most thematic on a paladin and nearly just as strong on one as on a bard or sorcerer. So why the hate on taking it on a 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.
I was going to get into specifics on HAM because I think you are underrating it's effectiveness even at higher levels but instead I'll use this opportunity to point out another one of my guiding principles. All the party contributes to damage. So even if you are doing double damage you aren't ending encounters twice as fast because you are still only increasing your party's damage output by a fraction of that.
However, when it comes to defense generally front line melee combatants are skewed toward actually taking a lot more attacks than their backline counterparts. As such that makes defensive abilities somewhat better than their percentages often appear. Likewise offensive abilities are often worse than their percentages appear.
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.
I totally agree here and it has the added benefit of not being DM dependent as Shield Master now after the last sage advice as often gets ruled favorably for offense as disfavorably.
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.
Not even 108% more as smites make up a sizable amount of your total daily damage and that number is basically flat between the 2 builds. Also even if that 108% was accurate it would drastically drop at level 5. It still isn't causing your party to do but maybe 30% more damage per round. It's good but it's not nearly as good as it appears.
But all this talk about offense has also got us ignoring the defensive benefits of the HAM protection style paladin. In the early levels HAM is probably reducing the damage you take by nearly half. The protection style itself is vastly increasing the survivability of any ally near the paladin. Honestly against many enemies at those levels it's nearly halving the number of times the ally is hit, effectively reducing their damage by nearly half as well.
At the end of the day I think offense is often overrated and defense(at least on front line characters) is often underrated.
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.
Back before the updated shield master ruling, I had developed a crit fishing paladin build that without buffs could nearly keep up in damage per day with a PAM + GWM Precision attack battle master fighter. On a fighter shield master isn't better than PAM + GWM but on a Paladin shield master offers very impressive offense when built correctly.