Problem with keeping the engine running and letting it starve it's self of fuel, is will you still have sufficient RPM's to feather the prop?
Most light twins you have to feather before the rpm drops below a certain figure, to make sure there is sufficient oil pressure. How much fuel is in the line how long will it take for the engine or fire to use it all, so when do you feather, you will be probably be focussed on whats going on, flying the plane making mayday call, do you recognise the running down and able to feather quick enough?
The fuel selector valve isn't in the engine compartment, it's at least behind the firewall, nearly all engine fire checklists require shut off the fuel valve, as you shutdown the engine it will remove most of the fuel left in the lines.
A 2014 incident with a Seneca showed that fuel valves may leak, current maintenance procedures do not require it to be checked or how to check it. So you could end up with more fuel being added to the fire.