That's actually pretty good reasoning and justification for it. I guess it comes down to what you would prefer when considering your first level feat, an element of defence and a safety shield that can help you throughout your entire career, or whenever or not you want to sacrifice some of your late-game/high-level defence potential, in order to give yourself a significant bump to your offensive capabilities at lower levels in order to help you get through the lower levels successfully to get to the higher levels.
After all, doesn't D&D typically follow the maxim that the best defence is a good offence?
Assuming no one else like a Bard or Warlock is taking it instead. But well reasoned.
Eeeeeeeh... I'm honestly pretty sceptical of this claim. They have to be right next to each other, and I've found a lot of combat encounters when people end up spread out and without anyone but their opponent directly adjacent to them. Might just be because of my limited experiences in these campaigns, but I don't think that gfb is reliable as people claim it to be at times. Especially as we are talking about Fire Damage here, with is infamous in how many creatures resist or are outright immune to it.
Not to say it is unreliable, just that I don't think it is as reliable as people want to believe it is.
Well, okay fine. Devotion Paladin can pick up Greater Weapon Master and swap the +2 Shield for massive damage potential. That's still only one type of Paladin. We still have Ancients, Crown and Conquest, possible Oathbreaker as well though I doubt that Oathbreaker is worth an actual discussion.
... Did, did you forget to add in the fact that a Vengeance Paladin gains Hunter's Mark's damage on the Polearm Master Attack? Because your calculations are pretty poor here.
STR 16 Paladin, going Oath of Vengeance at 3rd level for Hunter's Mark. Spear & Polearm Master vs Sword & IDK, Inspiring Leader.
Level's 1-2:
PAM: 1d6+3+1d4+3 = Average Damage is 12.
S&S: 1d8+3 = 7.5 Average Damage.
Sure, that's only a total increase of 4.5 damage. But this is level 1-2. HP is rarely above 20. That 4.5 damage is huge at this stage in the game.
Level's 3-4:
PAM: 2d6+3 + 1d4+1d6+3. Average Damage = 19
S&S: 1d8+1d6+3. Average Damage = 11.
And the difference jumped from 4.5 to 8. Which is a pretty significant boost to your DPR, and that difference only grows bigger if you get other stacking bonuses. Did you choose Dueling over Defence? +2 difference. Gone Oathbreaker, and hit level 7? Just got a +4-5 boon right there. Magic weapons? Sure that +1 doesn't mean much, but it does add up.
And then when you get to the higher levels, and you want to start throwing in Green-Flame Blade instead of just an attack Action? Well. If you're a Vengeance Paladin, for example, your quite likely to be looking at Haste. And did you know that Polearm Master's bonus action attack triggers off from Haste's Single Weapon Attack? It does count as an Attack Action after all. Meaning you can cast Green-Flame Blade, and still lash out with two different attacks chained together.
I think your underestimating how much of DPS increase PAM is.
Aaaaaand there's going a lot of your argument as well. As it has been ruled that Shield Master's shove can only be used after your attacks, and not before it. So going with 'RAW' is argunig that its DM Fiat, which is very subjective.