One of my favorite topics!
To answer the topic question, yes. And why? Because it seems like specialist Gods and Goddesses would care more about what ever you're praying for. That could mean they're extra wrathful, though, if you mess up, or just because. Sort of like Shintoism where the kami are in everything, so you should respect everything. Or like a corporation where tasks are sorted out in different departments.
Doesn't it sense for societies based on Greek/Roman forms of government to look at adopting their religions? When modeled after Rome, do as the Romans did? (Let's not talk about that whole collapsing bit.)
On the other hand, it is convenient to have one God to throw all your problems at, and of course he could handle it, being God.
I really couldn't agree more. If people find it unapproachable because they are not Roman or Greek, you could easily rename the same deities with American or more modern names and keep their functions exactly the same.
If I was going fishing i'd rather pray to a sea god than an overarching god. If I wanted a promotion i'd rather pray to the god of prosperity, et cetera. I don't see why they ever got rid of that system. It seems like an oversimplification to attribute everything to one deity.