Has there been any lore explanation as to why Almsivi and Divine intervention did not exist anymore in Oblivion and Skyrim?

Well, ALMSIVI is specific to Almalexia+SothaSil+Vivec (the Tribunal). These were gods specific to the Morrowind province. They were also kind of gone after Morrowind (game).

I'm not sure about Divine Intervention. Mark and Recall were also gone. I don't think Divine Intervention was really a divine spell anyway. It was just a specific Mark/Recall spell with divine flavor. I can't think of a Lore reason for this one.

Just like there are priestly healing spells, which are just regular healing spells with divine labels. Just flavor. I don't think TES really follows other RPGs that seperate priest spells and mage spells. They are all the same in TES. Priests and mages are basically using the same tools with different trappings/flavor.

We also got Fast Travel post-Morrowind (cue FT haters, gonna hate )

Yeah, allright Amsivi can thus be explained quite well.

But that still leaves no lore-friendly explanation why white people can't teleport?

P.S. : I am sorry for the lame joke.

It might just be an example of simple gameplay mechanics over lore - why would you want to teleport if you can fast travel?

Well, Beth was afraid of kids just warping away from all their precious encounters.

Isn't that just down to limited game mechanics? I liked to think guild mages relied on their understanding of natural science more often than not, while a priest used a prayer of sorts. So while "Spell Absorption" and "Vivec's Feast" had the same result, they were cast in different ways.