Faulty assumptions.
1. You assume my bonus action is free. I had great fun with a polearm master paladin. A GWM paladin can also have bonus action taken on any crit or kill.
You're right--the fact that the OP's houserule makes smiting cost a bonus action apparently confused me into discounting bonus actions for this whole thread, but in the context we're discussing them (comparison vs. healing under PHB rules) they are still relevant.
You don't mention it, but concentration is likewise obviously still relevant.
IME these are the main things that make smiting still a useful capability to have, sometimes: it has no action economy cost and no concentration cost. When smiting is a good idea, it's usually because one or both of these factors is in play.
2. Your opportunity cost involves spreading over multiple round. But the opportunity cost of THAT is not killing it faster. If round when when closing you cast a smite, then round 2 did multiple attacks, landing that smite and also Divine Smiting, the foe would often not get another action, especially with a ranged character helping. Denying a foe an entire action because it's dead is a greater debuff then the rider on either of those two first level smites.
You're kidding, right? Wrathful Smite, if it takes effect, is a one-hit kill for most intents and purposes. If killing the T-Rex on round 3 instead of round 4 is a big deal, then obviously disabling it (disadvantage on attacks and unable to move closer to you) on round 1 is even more relevant, wouldn't you say?
In the text I quote here you seem to be talking about an extremely weak foe (it dies after two attacks, with smite spell + Divine Smite, so I'm guessing it has around 50 HP), and unless it's a Flameskull and the party is in Fireball formation, it seems unlikely that such a weak foe is going to do enough damage in one round to justify a nova to kill it quickly. More likely it does 10-20 HP to someone, which you can just heal using the spells lots which otherwise would have been wasted on smites.
In the rare situation where you really do have to kill or disable the enemy nownownow, e.g. because most of the frontline PCs are fighting wolves at the front door but Strahd just decloaked (so to speak) and started murdering PCs in the back line--well, Strahd isn't vulnerable to Wrathful Smite due to legendary resistance, so a smite nova is worth considering. But it's not necessarily a better option than e.g. grappling him, especially if he's got something like Greater Invisibility up. Your top priority in this case is to take control of the situation, which means preventing Strahd from having free access to hit-and-run on the squishies.
At your table with house rules the balance can absolutely be different. I'm talking from the perspective of the rules in the book.
I'm open to arguments as to how allowing smite-after-crit is both (1) RAI and (2) significant to game balance, such that it materially increases the overall utility of Divine Smite (and therefore the OP's proposal). I've already explained why I don't expect to see such an argument--crits are rare, and the efficiency still isn't great even though it is better than a non-crit Divine Smite.
Fair point. I'll meet you halfway - it needs to kill them without any other PCs who would be able to do so before their next action. If a PC in melee halfway across the map goes, that's not too helpful. If the life cleric is the only other one to go and can't reliably do enough damage to drop him, same thing.
But yeah, if your friend the archer can finish him off then it's a bit of a cascade effect - that's someone else not hurt but who knows if that damage in the end would be > 70 points of healing, combat is far to chaotic to tell.
Yeah.
It would entirely nerf my polearm mastery paladin. It would hurt every single paladin with extra attack who has a reason to kill something QUICKLY. Remember, it's not always about HPs - maybe they need to slay them in 3 rounds to stop a ritual, or save the commoners, or whatever.
It would have a large effect on the paladin as a class, just not a large effect under your house rules and with HPs as the sole metric.
I don't think my house rules (and player preferences) have an impact here. Is smiting-only-on-a-crit really so crucial to your polearm paladin? It's happening only once in every twenty attacks after all, which likely means you're only smiting one to three times per day (a guesstimate--you tell me if it's wrong). That works out to six three- or four-round combats, and you making three attacks during every round.
I think that if you want to argue that smiting is central to the paladin's utility, you have to be smiting so frequently that my distaste for declaring smites after critting (which isn't even a house rule per se--the only time it came up, I didn't even have to open my mouth to say "Ew", the player just voluntarily refrained) would not be relevant.