To be honest, Angkor Wat is one of the weakest wonders out there. Specialists by themselves are rather mediocre and GProphets are a lot weaker than GScientists. Shrines can be decent, depending on what size of maps you are playing I guess, but it's really hard to compete with insta +1600

(=bulb) or +1300-2100

(=trade mission).
If you were allowed to complete only one wonder, in most games it would be between Mids and GLH for me. They are the only (early) two wonders with game-changing powers I think. Even they are map dependent, goes without saying.
I don't know, keeping a GProphet (likely from Oracle) handy to bulb Theology for trade bait among a group of non-zealots works alright every now and then, you can bulb CS or CoL quickly with the right set up...Hagia is also actually good on Huge/Marathon games so quick access to that gives a good shot at it to speed all development your workers do in a game where chopping a forest costs 9 worker turns, roads take 6, etc. They make a good fallback method for triggering the first golden age if the Music artist is out of the question. Admittedly fast CoL is not really worth it compared to simple Writing-granted Scientists especially when it takes away Slavery, and it doesn't trade well. Of course this lensed like always by difficulty levels, it may not hold up going higher than where I play.
As for running priest specialists to get one? Ew. That requires both spreading a religion and building a temple early on. Maybe something viable for Egypt. Rather work a better specialist, a good tile, or whip that pop away before doing that. There is an odd state of the game where you might not have forges for an Engineer yet and then, improved with AW, they are better than nothing in low hammer spots. But generally the worst Specialist with the exception of Spy IMO.
The only wonder I consider in every game, ever, at all, is the Mids. Not even Oracle or GLH, even Kremlin is so impactful; a game with early access to Police State, Rep, and (less so) US is a different game entirely. Like all wonders it won't make or break your game but there is a definite distinction between having it and not. I agree with GLH making a similarly large impact,
potentially, but it's so crazily situational: whether you have a spot to snag it first, the leader pool (Kublai and Joao love to build it as an example, yourself being non-IND will hurt your chances, etc) whether you can settle enough coast to make it worthwhile, whether the map has lots of other landmasses to justify it, etc. Mids is like "oh, now I have free Rep at 1000BC, nice" and can be compounded through running scientists everywhere, etc. At the very least I'd value the Mids so much more highly as a captured prize; I'd give back GLH or burn it without much hesitation unless it's one of the maps extremely conducive to having it (Archipelago, etc).