Just take your accelerometer's reading and multiply it by the current mass estimate?
That is not a good idea. I'll start with launch, where using sensed acceleration wouldn't work at all. Launch vehicles are held down by hold-down clamps until engine ignition is confirmed. Most launch vehicles shut themselves down if ignition is not confirmed. An accelerometer is useless for this because the hold-down clamps prevent the vehicle from accelerating upward.
The solution is to use multiple sensors. Flow rate sensors, combustion chamber pressure sensors, combustion chamber temperature sensors, ... The key problem here is that sensors can and do fail. The combustion chamber in particular is a very hostile environment. The Space Shuttle experienced multiple Redundant Set Launch Sequencer (RSLS) aborts, at least one of which was caused by sensor failures rather than effector failures.
Once a vehicle has launched, accelerometer readings can provide clues regarding main engine failures, but only clues. The propulsion system / thruster sensors that are need to confirm ignition provide better clues, so long as those sensors haven't failed. The solution is to use reliable sensors that are unlikely to fail, and redundant sensors in case one does fail.