Last common ancestor lived around 80 million years ago so "distant" compared to how close people expect them to be. "Distant" and "close" are generally relative terms. So alligators and crocodiles split off just a little bit of time (in evolutionary terms) after placental mammals and marsupials split from each other, which are generally considered to be distantly related to each other (relatively speaking, and especially useful when explaining to someone that the flying squirrel and the sugar glider are not close).

The earliest known whale ancestor that wasn't itself a cetacean is known from around 50 million years ago. It looked like a dog/raccoon and lived on land. Alligators and crocodiles split off more than 1.5x further back in time compared to then.

Finally, and this may blow your mind, at the time alligators and crocodiles last shared a common ancestors, humans and pigs also shared a common ancestor. So yes, I would reiterate that crocodiles and alligators are distantly related.

Look man it's clearly dead. It has ceased to be, it's kicked the bucket, it has gone to meet its maker. This, is an ex-bird.

That's an interesting possibility, but the only issue is we don't have any concrete evidence on how or why predatory pressures are different on young alligators compared to young crocodiles (though I realise everything we are discussing here is conjecture anyway). According to what we know today, both alligators and crocodiles are vulnerable to predators as juveniles.

I have my own hypothesis, which I've added in a comment under this post just now. Lmk if you have any thoughts.

OP here attempting to answer my own question, lmk what you think if you want to.

It is my understanding that alligatoridae (or at least the direct ancestors of the two extant species of alligators that survive today) evolved, on average, in considerably colder climates than the ancestors of crocodilidae (the oldest alligatorid fossil currently is from Alberta, Canada). It's a known fact that alligators can take significantly colder temperatures than crocodiles, including but not restricted to the fact that alligators are able to survive short periods of living in frozen swamps in the peak of winter, by sticking their snouts above the ice and going into a sort of inactivity. Crocodiles can't do anything close to that. Since "over-wintering" is a thing for alligators, where they go into longish periods of inactivity/brumation, I would assume that the tail would provide a vital reserve of fat etc to burn through while they're in that state. For a larger, robust animal, it might not make enough of a difference to persist evolutionarily, but for a juvenile with a small body, that extra reserve of fat might be (or might have been in the recent past) the make or break factor that decides whether it survives a period of inactivity or not.

Of course, regrowing a tail even partially is resource-exhaustive in itself, but if they can time it right (I mean reptile metabolism slows down in the cold so if they're regrowing it they're probably doing the bulk of it in warmer weather anyway), there are probably some benefits to be had that outweigh the losses.

The fact that the regrowth is only partial and imperfect might point to the fact the benefits were considerably more relevant at some point in the recent past (ice ages?) than they are now, whereas those same benefits probably haven't been relevant at all for a long time for crocodiles, which have mostly persisted in warmer climates throughout the recent past.

Would love to hear feedback/thoughts on this, or if anyone has anything to add.

Don't agree with that. Since no one was around to physically witness the evolution of any species, that would mean that our ideas on why any two species that shared a common ancestor evolved differently over time would just be generic statements. But in fact there are many such cases where one (by that I mean scientists, academicians) can make strong, educated guesses based on multiple factors like the fossil record, climatic differences, predators etc.

For example, the orangutans in Sumatra (especially the recently classified Tapanuli orangutan) are almost entirely arboreal whereas the Borneo orangutan is comparatively more comfortable on the ground. The educated understanding of the scientific community is that this likely happened because Sumatran orangutans evolved in close proximity to Sumatran tigers, unlike the Borneo species. That's not a generic answer and is certainly an interesting thing to ponder on.

That's the kind of thing I was looking for (to arrive at a probable/possible answer based on current evidence, if there is any). Not "tell me what the exact reason is, I want the exact reason!" I know you can't often find objective answers like that when it's evolutionary biology you're talking about.

But that makes the statement distinguishing the terrestrial apes and arboreal apes in terms of the shape of their clavicles meaningless. Because there are really only two terrestrial apes (gorillas and humans), and one of those two doesn't fit what the statement claims. So why make that distinction in the first place.

But then humans are terrestrial apes, not arboreal apes. So why do we have S shaped clavicles like chimpanzees?

I was with you till the last couple of paragraphs where I was like nope. Birds aren't just descendants of theropods. They are theropods. And even going by what you are saying, many of the animals that anyone in their right mind would unequivocally and definitely categorise as both dinosaurs and theropods (such as raptors, T-Rex etc) had hips that were definitely not like lizards, but very much resembling those of modern birds. So they shouldn't be called saurischians either, but according to you it would be scientific pedantry to call them dinosaurs as well, because it was really their distant ancestors that actually had lizard like hips. No, I'm pretty sure that's not the correct way to approach it.

I think your understanding of cladistics is a bit erroneous, and what I'm gathering is that the saurischian and ornithiscian distinction might be dated (or based on superficial similarities). But I have studied enough about the question of birds being dinosaurs or not (by "not", I mean if it's really pedantry to call them that), and I can tell you it's not pedantry in any way shape or form unless you want to bring into question the whole group of animals called dinosaurs in general. Birds aren't distant descendants of dinosaurs, nor is it misleading to call them dinosaurs. They are dinosaurs.

What I fail to understand is how birds can be said to have hips like those of lizards, and not like those of birds

Leg position (under or beside the body) is definitely not what distinguishes saurischians from ornithiscians. It's to do with pelvic structure and the position of the pubis bone.

And birds are saurischians. This is from Wikipedia:

All carnivorous dinosaurs (certain types of theropods) are traditionally classified as saurischians, as are all of the birds and one of the two primary lineages of herbivorous dinosaurs, the sauropodomorphs. At the end of the Cretaceous Period, all saurischians except the birds became extinct in the course of the Cretaceous–Paleogene extinction event. Birds, as direct descendants of one group of theropod dinosaurs, are a sub-clade of saurischian dinosaurs in phylogenetic classification.