Or even just drop the bulkheads and turn off the turbolifts? It'd take a week for the boarding party to zap their way to the bridge. (Accommodating of them to beam into a transporter room, and not right onto the bridge, incidentally.)
None of it makes too much sense, but perhaps auto-destruct and intruder containment were some of the systems damaged in the BoP attack. Lots of other things already went gaflooey, and Kirk & Co. no longer had any hope of running the ship themselves.
So the only hope was destroying the bridge and (more far more importantly) computer core, and letting the atmosphere do the rest of the work.