"why religions?": it's a good question!!
Maybe the best answer doesn't come from our social model but from the govt and riots models. The historical high influence and power the church has had in govt decisions is IMO the most important reason to have religions in the game. Also, being religion a central part of people's life in ancient time but not in present times has important consequences for what type of govts the people is willing to accept. You can't put a divine monarchy in today's Germany and expect it to work.
Finally, religious discrimination through history has had an impact on the development of certain groups compared to others not discriminated. It has also created revolts and other major social events such as the creation of new nations (Pakistan).
Corruption: The ideas you have cited sound good, but do consider that in the social model we're trying to determine the corruption level of the "average man" in order to simulate how a society (from top to bottom) can be more corrupt than other. Average man's corruption may help us simulate, for example, tax evasion. You seem to be focusing on the ruler and the guys with power. What we can do is incorporate your ideas of govt corruption in the govt model, specially in the part of "spending public funds" (not yet developed). In a corrupt govt some money would be "lost" due to corruption.