You know, I’ve seen the same thing. Other than the cleric, most PCs in my group would rather attack than take a round to stabilize a dying companion. Some in my group just charge in without any strategy or thoughts of working as a team. The most recent character death was directly a result of the group not working together, and it was almost a TPK.
And in Adventurer’s League play, it seems like my bard ends up responsible for healing magic much of the time.
I’m not sure what gives. For me, it started in 4e, when most characters got to be nigh-invincible. But I don’t know if that’s just a timing issue, or an actual root cause.
There's maybe been a pendulum swing going - assuming you're playing the latest ed, that is. Last edition, the game got very group-focused - group tactics, abilities that helped allies, defined 'roles' that contributed to group success, and involved 'set piece' combats that called for all that. Latest edition generally tries hard to be everything the last one wasn't, so none of that - individual tactics & abilities, self-contained characters, small/fast combats that don't require synergy to defeat.I'm finding the opposite, it seems to be more with players who had exposure to previous editions. The younger folks I've gamed with don't seem to have any expectations. I've actually seen several friends I've known for 10 or 20 years move to this type of play style, and if they are regular MMO players, the problem gets far, far worse.
As a DM, I believe it's better to give players what they want rather than 'teach' them the 'right' way to play, but that's just me. You could give them harder challenges that require teamwork to overcome - it may just be that they're not engaging because it's 'too easy' (not a rare complaint lately). On the other extreme, you could give them more scenarios that offer a chance to compete, even while working towards a common goal. Making who scores the 'killing blow' on a monster important somehow (exp, renown or some more tangible reward, like finding a magic item on it or receiving some special ability from it's 'heart's blood' or something), for instance, means they cooperate, but are also racing eachother.How do I deal with players like this? Kick them out? On the other side of the coin, what if I'm stuck at a table (or worse, a table at a con) with one of these people?
But I have to wonder... A friend of mine plays a lot of indie games, and her players would be, in D&D terms, incompetent. They always split up, give tasks to unsuited PCs, and so forth. Her stories sound hilarious, but I doubt I'd have much fun playing in one.
When we play with them and their younger friends it literally takes an act of congress/parting of the red sea/meteor strike to pull them out of their smart phones when it is not their exact turn, or if it is during a part of the game where nothing is directly impacting their characters.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.