(I'm ignoring the novel Crossover, which had Scotty bootstrap a cloaking device onto a Constitution class ship)
But it wasn't a Connie running at full capacity. IIRC, he was running it on full automation and was the only person aboard. So its power systems would've been down to bare minimum and the cloak would've been viable at least to a limited degree.
Steve Mollmann wrote:
It was the cloak from "Enterprise Incident", though, and we know from that very episode that that model of cloak could conceal a Constitution-class starship.
At least it could briefly. And again, maybe the power systems were cut down to minimum. I'm not saying it's physically impossible to cloak a Starfleet vessel, just that the intended functions and mission profiles of most Starfleet vessels are incompatible with the use of cloaks, that you have to trade off so much functionality to make the cloak viable that it's just not worth the trouble to have a cloak as a standard component.