I'm thinking if HoMM was RTS instead of turn-based it would be about what I had in mind.
Pretty much the same for Fallen Enchantress, now that I look at it a bit closer. I have Warlock: Master of the Arcane and while it's fairly fun the whole turn-based gameplay has lost its appeal for me. I'd much rather have everything just happening in real time rather than having to take turns playing.
The game I referenced, Clash of Clans, to me seems like one of the RTS Warcraft games but with multiplayer thrown in in discrete portions. Build your base, build your army, then raid other players' bases and try to overwhelm their defensive setup. And hope that your own defenses are good enough to block other players from leveling your base while you're offline. Your base/defenses get better over time as you take more resources from other players but the opponents you face get better too so it stays pretty well balanced.