Why is there no alert if shutting down a running engine during flight?
Because in an emergency situation you do not want to stand in the way of the pilot.(*)

Whoever designs the system knows that it could fail and it also knows that there are two pilots in the cabin. These pilots have been trained to deal with the emergency, have spent hours and hours in simulators to be ready when something happens, you do not want to treat them as clueless users, you want to treat them as professionals that are doing their jobs.

The system told them that there was a failure, if it would have been a black/white decision the system could have already shut off the engine, but it did not: it lets trained personnel to asses the situation and act accordingly.



*: as fooot correctly points out, you do not want to annoy the pilots with warnings (remember, you just told them an engine is not working!), they may be tempted to preemptively cancel them, causing them to miss other warnings that are actually important.