I looked at Runbox. Their offering does not satisfy my requirement "where price is not per account but per domain with unlimited or large number of accounts".
What they have is a main account with lots of aliases, but each separate user account, which they call "subaccount" is extra pay.
I have asked a similar question, and was pointed to your response here. From what I see at Migadu's site, it is a good service. Currently the top of my list, but the research is ongoing
Do you mean web apps? Today they are powerful, but in 2008 browsers based web apps could not have access to a lot of things native apps could, I think, so native was inevitable, hence the AppStore.