It isn't true that big creatures always had maintenance costs.
From the top of my head, Craw Wurm is a big creature from Alpha with no upkeep cost or even a real disadvantage (if you exclude the high casting cost).
In fact, looking at all the Alpha creatures with stats bigger that 3/3, only Demonic Hordes, Force of Nature and Lord of the Pit (three of them) have such maintenance costs!
This being said, it is true that big demons in magic are known to have certain characteristics: big black creatures with upkeep costs. In fact I think Mark Rosewater mentioned in an article that they acknowledge that fact when designing demons (I can't find the article, mostly because WotC is doing server maintenance right now. If you're interested I can google for it later and edit the answer).