Why do people keep talking about the risk of going for a religion? That is obvious. My post has nothing to do with the risk involved in going for an early religion, my post is questioning the value of getting one. Assume that you WILL get Hindu, Budd, or Jud if you go for it. Even knowing that you will be successful, is it worthwhile?
I'm not sure that there's enough, but it might look something like this: early religion is a big culture boost. Cities that are "near" the capital can ignore worrying about culture, either because the holy city has already claimed the interesting resource.
On picking up Mediation, you also have the option of transferring culture (via missionaries). You also have the option of constructing a monastery, which is a cheap culture building that's actually provides additional return on the investment.
The early religions also give you the option of a cash cow in your capital, without having to jump through hoops (delaying other settlements, or palace-porting) to achieve it.
A perfect storm for Meditation might be the conditions under which you can land it plus gold. Gold -> early commerce -> early research -> lots of science to push through the monastery multiplier. With gold in pocket, you are nicely placed to the ignore the religion tree and concentrate your efforts on the Shadowan Paya, and use that wonder to unlock your civics (and prophet points).
Monotheism is a bit harder - I wouldn't want to gun that tech without having some sense of what's kind of hand you have been dealt. But that does give you a builder boost right away, so if your plans were vertical, rather than horizontal (ie - I had to pick up Masonry to get here, I might as well grab pyramids) you've got some synergy. No neighbors, or very secular neighbors, would probably be a piece of this puzzle too, taking advantage of the fact that the single religion could keep the dogs on the leash.
Poly is hardest to justify, I think. It's got the same border pop, early spread cred; but you have to make the call before you have a lot of information about your circumstance, and you can't spread the damn thing without additional religious study. Sure, if you have marble within reach (or better still, just out of reach except for the holy city culture boost), so that you want a shot at those wonders anyway, you might as well grab the brass ring as well.
At one point, Poly also had the advantage that the AI was less likely to research that direction out of the box. I haven't checked the math on this in a long time, though.