I played a few AP champions I didn't have any mana regen issues at all and I did spam them, with the right masteries / runes / items you shouldn't have a problem...

Agreed

I had mana issues on Blitz (first couple times out... obviously you build lots of mana on him and it wasn't a problem by late game) and Jarvan (uses more mana than many casters, and there's no blue buff now), but no problems with the rest of my champs.

I DO however think they should double the growth rate of tear items, as well as farming skills (Nasus, Veigar, etc.).

RoA still shows as a recommended item for some champs in Dominion. There's a reason for that. If you're having mana problems, take a look at your masteries/runes. Also, casters in Dominion serve better as defenders. Pick a base near your nexus, knowing you can port back in under 5 seconds for a recharge. Am I missing something?

If you're spamming Kassadin's R, you will run out of mana regardless. I don't see what your point is.

In Dominion everyone has a mini blue buff at all time.

I played swain one game, it was so dumb. I even took clarity, ran out of mana so fast and was rendered useless before I could do anything