I agree with you for nearly everything you said!That's one option. The other is to claim under your own house insurance and your insurers will attempt to recover their costs from the tradesman.
All the advice in this thread is for the typical case. You need to check your own insurance and the terms and conditions attached to the contract you have with the plumber and probably consult a lawyer to be absolutely sure what applies in your own specific circumstances.
You need to check the credentials and experience of any plumber you employ. It is not a regulated profession so there are some cowboys. Best to go with a local firm that's been in business for a significant time and employs properly trained people. You want their reputation to be "quite expensive, careful work, excellent result" not "lowest quote, fast work, corners cut"
Also, unless you have a lot of time on your hands, it's not worth kicking up a fuss for work that's only going to cost a couple of hundred quid to have put right by someone competent. Write it off to experience and be careful to check the reputation of anyone who you use in future.
Actually, as a customer, personally, I don't mind paying more for some competent tradesman to do a trouble-free job, he gets paid I have no issue left!---I wish I had a crystal ball!
However, it is difficult to choose the right person, for example, I normally find tradesman on Checkatrade, I check reviews first, the issue is everyone seems have good reviews....