At that level, it is simply unnecessary bloat. Any and all religion qualified you for those civics; Why should there be more than one religion if all are the same? Why should religion exist at all rather than simply as those civics?
What you describe is not depth, it is purely unnecessary complexity. There is no tradeoff, no weighing of options, no depth. Just a few extra clicks, hurdles to jump through.
Notice that religion still exists in the Piety social policy branch, much as you describe with civics; Same principle, minus the bloat.
Edit: For an example of real depth in a religion mechanic, check FfH or any of it's modmods; Each religion has significant effects on how you play the game, and choice of religion is a
very important part of playing. And this STILL isn't as much depth as I would like in the mechanic.
You were forced to devote commerce to accumulating espionage, or your opponents would have a significant advantage. At the same time, making use of it yourself lowers your ratio with the enemy, leaving you, again, vulnerable to enemy attacks.
Forced to put into it, penalized for using it. Horrible mechanic. Rather than go too far into it, just check this old design doc out; Outlines many of my issues with the system and how I would change it. Never happened, likely never will, but oh well.
https://docs.google.com/Doc?docid=0AdALd3TwFjopZGhqdzVrajZfMjFoZnI3NjJmcQ&hl=en