I could also insist that the copper pipes - as contractually agreed - be installed, couldn't I? It's my right to receive what I have paid for or what was agreed upon. Or am I wrong?
It's not that simple. You could (and should) have insisted during installation that copper pipes be installed according to the contract. Afterwards, it depends. If the installed material is unusable for the intended purpose, it will likely have to be replaced. However, if the material is common for that purpose (just cheaper), you cannot necessarily demand a replacement; it depends on proportionality and the scope of the work. If you cannot assess or quantify this yourself, I would suggest involving an expert who can financially evaluate the defects. Based on that, you can then talk with the general contractor.