Forgive me if this has been discussed.
I almost feel aasimar and orcs are the replacement for half-elf and half-orc, thematically.
So what is the story beat for a half-elf? Traditionally, its a person born between two worlds; human and elf. The human represents a common ancestry, the elf a more refined and elegant one. The elves want little to do with the half-breed, the humans fear his strange features and abilities. If you replace "human" with "mortal" and "elf" with celestial, the beats pretty much work the same. The mortal side either respects or fears the celestial origin of the aasimar, the celestial side looks down with pity on their mortal and imperfect offspring. They still end up children of two-worlds, never fitting in either, but the origin is now magical rather than biological.
Likewise, the story of the half-orc is that its a PC orc race with its savage and bloodthirsty tendencies tempered by a hearty dose of human DNA. An orc people still have prejudice about, but, is acceptable in more civil society. So PC orcs do the same, but without the need to breed out the bad genes with human genetics. Some orcs are just good people and don't need a human parent for that to be. They get the same reaction that most people have to half-orcs, be that good or ill.
Does that solve the problem? Not 100%, but I do think the two races can be use to more-or-less create similar storylines to the half-races without getting involved in Punnett squares. Aasimar are half-elves, but with aloof parents that truly are exemplary of goodness, beauty, and grace, while orcs can fill the role that half-orcs did but without having to breed the orc out of them first.