Yes, the opening pressure
can drop from fatigue.
I have an 89 Jetta with 350,000+ miles. This winter I replaced the injectors with Reman'd Bosch. The old ones were originals with VW and Audi logos stamped on them and looked way better than expected when pulled

. But needed new nozzles or nozzle cleaning prep at minimum.
I can't say whether or not they had been rebuilt at some time or not - but i was surprised to see those logos when i cleaned them up a bit after removal. Those are only used on the production/assembly line.
Since the new parts were in hand - and i wanted to do the car a favor anyway - i put the new ones in.
The only difference the new Remand's made was it quite burning oil under driving conditions, and low speed off idle grunt was just a lil better. Which is what i was after anyway - but had hopes of even better results than that.
I could have just swapped nozzles and probably been just as well off. Pure Judgement Call as to which way to go.
If you have other things to drive and can let the car be down a few extra days - you could take old injectors to a diesel shop and have them pop-tested first. If they were in range - i'd just do nozzles on my own.
Having a shop rebuild them and apply new Bosch nozzles and setting proper specs will cost as much - likely more - than buying through AhausAZ. Most will charge premium retail for nozzles. Some 'might' let you supply your own nozzles. But all that gets tricky with them sometimes.
You can have several options if you are not in a rush on downtime.