It comes down to cost and zoning/permitting. It's much easier to get a permit to run a generator for backup use than to run one 24x7. It's also hard to get a 1-10MW plant which is per-KWh as efficient/inexpensive as the grid (although now that natural gas is about 20% of what it was when I last bought it, gas turbines actually are cheaper than industrial tariff grid power, if you have good gas access...). Being able to actually use the waste heat is what makes the combined cycle efficiency worth it.
There was a crazy plan to run a datacenter on a barge tethered to the SF waterfront, for a variety of reasons, but a primary one being power -- the SF city government wouldn't be able to regulate the engines/generators on a ship running 24x7.