That doesn't happen because most start-ups don't think most support roles are worth it until one of two things happens: Management gets tired of losing people to 24-hour on-call rotations or the company gets big enough that "the devs who wrote this stuff should be able to get some sleep" becomes a valid consideration. Almost every aux position is considered "needless" until, well, it isn't. Granted, I say this from being in the Operations and Support worlds for years since I get to see the other side of not having a functioning Ops model before making it big.
I think by support it's more the office manager, cooks, call-center style customer support, etc. Ops is pretty core to any software company that has servers.