If the flow is blocked, how do you check that the pump is ON ?
Yes, if nothing is moving in a hydraulic system, there should be no flow to the actuators. And, especially if the pump is a variable displacement (swashplate) pump it will "stroke off" like it is supposed to so as not to be making oil at pressure when it is not needed. Now if the pump is constant volume like a bent axis or gear pump there would then be flow over the relief but how much do you look for? When things are moving, you'll get most of the flow to the system and only a little or none over the relief and vice verca when things are not moving.
Now, maybe you have a hydraulic motor that runs all the time, then, yes, a flow switch or sensor would be great.
If you just have cylinders, rotary actuators and grippers then put switches on all the positions. Time each move and generate an alarm if the move doesn't occur in the expected amount of time (plus a little to avoid nuisance trips).
If you want to check for system leaks, put flow meters on the line to the actuators and the return from the actuators. Check that the flow out equals the flow back in (kind of like a GFCI in the electrical world). I suspect you'd have to play with the settings on this to make it work practically and not nuisance trip, especially if there is an accumulator in the system. You'd probably need timers on both sides (start of motion and end of motion) to account for the accumulator emptying and filling not to mention you couldn't look for an EXACT match on analog signals but just that they are close to one another due to the usual sensor and system built in errors.
Anyway, I think looking at the actual end effectors is best as that is the reason for the system in the first place. If you can wait until a move doesn't complete to flag an error then the position switch/timer method should work for you. If you need to know something is wrong right away you will need to put feedback devices on the moving elements and check those for motion. The type would depend on the motions you are making and the space and budget you have.
These are just some ideas off the top of my head with the limited information we have here. As always, give us more info... get more answer...