There are very few "immortal" species, and that trait has not given those species a huge edge in population growth. Thus the trait did not allow them to outcompete "mortal" species, which means that the blind chance of evolution lead to the "mortal" species being progenitors of most life.
Well not quite, dying is a feature, not a bug.
Being immortal is actually a very bad thing for a species since A) Having dudes that stick around forever hogging resources due to being there first without evolving until something unexpected is bad for future generations, B) Having these immortal dudes plopping out babies generations later is bad since they aren't evolving and its also important to note that C) No matter how "immortal" these dudes are in normal circumstances eventually diseases are going to evolve or the environment will massively change and they won't be able to adapt and them and everyone else within a few "generations" of them are all going to die at once.
So these immortals are all going to die anyways, and probably en-masse when something major changes. Note that this stuff holds true on every level, from the single-cell all the way up to the largest creatures; immortality is simply a bad evolutionary bet.
So if we do manage to get immortality as a species (which is quite possible although humans, like nearly every other living thing is designed to die) the natural equilibrium is going to be thrown even further out of wack then we already threw it. Immortality almost certainly will result in *really* bad stuff for a lot of humans due to how it will throw off resource distribution.
In modern times, if everyone were immortal, I think there'd be a beneficial interaction with capitalism and democracy that'd help prevent some of the pitfalls. Obviously, if everyone lives forever, then shortsightedness would probably be considered the worst sin you could possibly commit. There'd be no "Fuck you got mine" with all these people that flout climate change, because instead of not having to worry about the consequences, you will have to worry because you WILL live to see those consequences kill you.
Moreover, there'd be no "Boomer" generation that is disproportionately larger than other generations, because if the way that the Immortality works is that you simply stop aging at some point in your 20's, and from that point on you simply live forever until killed by something, then voting demographics wouldn't have one large group of assholes that are ruining democracy for everyone else by selfishly voting for their own interests to the exclusion of everyone else. Everyone would be voting on the assumption that, hey, we're all going to be around for a while, so let's vote with that in mind.
Moreover, an immortal society wouldn't need to worry about retirement rates or replacement rates, or atleast not nearly as much. People probably wouldn't be thrilled about working at shitty jobs for the rest of eternity, so I can imagine that highly socialist platforms like UBI, worker protections, etc, would be nigh-universally agreed upon.
Marketing in an immortal society would probably get pretty unusual. Most marketing uses age-groups, but in an immortal society that has been around for a while, the majority of the population is going to be very old. So instead of age-groups of like 18-30, 30-50, etc; we'd have age-groups 18-100, 101-300, 301-500, 501-1000, 1000+, and so on.
Though I imagine that immortal biology would have to be optimized for living for very long periods of time. The most major concern would probably be memory capacity: Even if you live forever, that doesn't mean that there's infinite space in your brain to store all your memories. Everything in your brain has to be physically stored with your brain cells, and while a human's memory capacity is enormous, it's still finite. I imagine there'd be an approximate cap to a human's age, where they'd inevitably start to experience anterograde amnesia, where they can't form new long term memories; or start to experience a kind of retrograde amnesia, where old memories are destroyed in order to create new ones, and so the oldest immortals in fact cannot remember the majority of their long long lives.