Its a tough one and there is always 2 sides to every story i suspect.
It reads to me like its a new ground and maybe things are tight investment / cash flow wise and they need to do this till things improve and they get on their feet.
Picking up clays and re-using happens all over the country in my experience at a lot of grounds and trap breakdowns just happen now and again. The reality is that these traps are hooked up onto the back of quads / trailers - driven out to their location, stood out in a field in all weathers with these discs that cost probably fractions of pence to produce and are sold to the grounds for single figure pence. Then they are flung across the sky at several mph from these mechanical traps.
Then we expect them to perform flawlessly every single time - not bloomin' likely.
Now i do cringe when i see traps full of clays (new or pick ups) being driven around and bounced through fields as inevitably some will break. Would that be more likely to happen using pick ups - probably yes - but all it needs is time and experience and the ground owner will learn this. Much more cost effective to empty the trap prior to moving it if the move is going to be bumpy.
As long as your not being asked to pay for broken clays / its not a competition then no harm no foul IMO.
My regular ground 100% does not use pick ups for his registered targets but on his club practice - yeah why not - end of the day he only charges members 23p a clay for practice and out of that he needs to buy various types of clays that will cost more than the typical 6 or 7 pence each for a standard.... Rabbits, Mini's, Midi's, Battue's as well as various differing colours. Then he has to pay staff wages, overheads and then finally that dirty word - make a profit.
In case of breakdowns / no birds there is a clear disclaimer on every stand - More than a single no bird from a trap. Stop shooting and call the given mobile number and someone will come and look at the trap for you.
The other side of the coin relates to another topic for ground owners and one i see in the "news monkey" section this morning - shooters taking the pee and stealing targets that they are not paying to shoot.
This was rife at the same above club till June last year when they installed the promatic card system and the above no bird system as now you paid for EVERY target on the card at the end of shooting / no ifs, buts or maybe's - if you kept pushing the button on "no birds" or every shooter wants to "see a pair" instead of watching the person in front then that is your own silly fault - no sympathy unless you followed the instructions on "no birds" given on every stand and prior to starting shooting.
Took a while to get used to for some and the owner has had to give a little also - for example you get 27 targets on skeet to allow you to either "see a target" or in case of a no bird allow you to complete the round without calling the owner. Funny thing is now particularly on the skeet you go to the card machine and you can see those extra targets build up over the day where people have not had an issue - shot their 25 and left the spares on the counter.
Result was he had a few moaners "I'm never coming here again your taking the mickey" etc etc - but despite that numbers of clays used dropped and yet profits were up. So much so he was able to drop the prices he charged from 24p per clay to 23p per clay for members and even also offered the same reduction (28p to 27p) to non members and also reduce his registered price by £1 a hundred.
It made that much difference with the amount of clays being stolen. Its no wonder that grounds use "pick ups" if that situation is being mimicked across the whole country.