I think they put tieflings in 4e because it was a fairly popular race in 3e (and in Planescape (Torment or p&p); who does not love Annah?)
They appear as interesting figures in some 3e FR novels. They even had representatives in the Baldur's Gate games.
Aasimar never garnered such popularity.
I think the fact that tieflings had more cachet than aasimar certainly plays into why they were in 4e (which was pretty explicitly interested in milking new brand identity from old phrases), but regardless of the merits or flaws in that chain of thought, they remain in 5e, I think, largely because 5e doesn't reject 4e, it evolves from it. You liked your tiefling warlock in 4e? Okay, the same archetype exists in 5e (even if it is quite a different mechanical representation).
Why? Well, conflicts are interesting. Somebody fighting their evil upbringing and heritage to do basically good stuff is a lot more interesting than a being of goodness doing good stuff. (See Driz'zt.)
It could be interesting to see a story about an aasimar battling his nature to do evil would do it. But stories with evil main protagonists tend to be boring.
Eh. Aasimar can be interesting. They make fascinating villains in Planescape (influential, respected, and totally assured that their own view is completely and utterly right because they've never really been told anything different). They also make interesting characters in that setting -- wrestling with society's expectations of you and your own limits, or asking what is "Good" about you just because you are born with eyes of liquid gold.
I mean, lets not confuse popularity with quality, or we should all just be playing The Drizzt Do'Urden Game of Wangst And Weird Sexual Stuff because that is clearly the Best.
But tieflings were certainly more popular than aasimar in the run up to 4e, and while I can't speak to what "everyone" liked about them, what
I liked about them was their status as outcasts, heroes who fought against (or played within) society's negative expectation of them, exploring concepts like racism, classism, physical and mental handicaps, and otherization. Which isn't exactly comfortably compatible with 4e's vision of them as an internally consistent people with one true origin.
And what I like about aasimar is also that toying with otherization but from the other side -- having high expectations that you can't possibly meet, being put on a pedestal for what you are, being used like a trophy in someone else's mind games. Not being any different from other people but having people constantly put stuff on your plate -- or try to take you down -- because they think you are trying to be or somehow are "better" than them. That can be as alienating as people thinking you're a vile and untouchable unfortunate.
The devas in 4e don't capture that vibe, either. Like the tieflings, they have their own story.
That's ultimately why I went with developing a separate Planetouched race. Aasimar, tiefling, genasi...the themes I want to explore with these characters are similar, just slightly different reflections of it.
Ultimately, though, the goal of the 5e PHB was not "present am equal distribution of iconic Good Guys and iconic Shady Characters for use as PC's." It was probably first and foremost, "If it's in a previous PHB, we should put some reflection of it in the 5e PHB." I wouldn't be surprised if at one point they were like, "Death Priests OR Necromancers, guys, we can have one or the other, but they overlap a lot, and both also make good villains, so one of them is going into the DMG."
Death Priest loses in that comparison because it's a little less flexible -- previous Death Priests in D&D PHB's past leaned toward a "must be evil" requirement in a way that necromancer wizards did not.
