The other reason you don't shut a running (or partially running) engine down like that, even if it's displaying a fire warning, is that you'll lose the services it provides in the form of electrical power and hydraulics.
On Concorde the undercarriage is operated by the 'green' hydraulic system. The 'Green' system is driven by pumps on engines 1 & 2. Shutting down No.2 when No.1 had failed meant they could not raise the gear, greatly adding to the drag.