BBQ - Construction-accompanying Quality Control

Where people work, mistakes happen. That is completely normal and not a big deal. Even the best and most reliable (construction) contractor can overlook something. With such a huge investment as building a house means, in my opinion, you cannot secure yourself enough.
If it's about the trust relationship with the GU: simply communicate openly and make it clear that this is not a measure based on your distrust of him. You simply want any possible mistakes – which, as mentioned, can happen to anyone – to be discovered as safely and as early as possible.
And if he is really a good one, he won’t have any problem with that...

What reasons speak against it?

It's not about the money, and the general contractor has made it clear that it is not a problem for him. It's more that it's a bit of additional stress for me and also for the general contractor.

Your [GU] has already stated that they see no problem with it. It is really more that it poses fewer problems for him and you. In our case, all services were properly carried out by the [GU]'s permanently employed staff. The mistakes were made by the [Subs]. Here too, a decades-long contractual relationship existed between the [GU] and the [Subs]. A little anecdote: our [GU] spent two days kneeling together with his wife installing the insulation for the floor and explained that he preferred to do it himself because he knew the quality of the work...

@ALL

Thank you for the clear feedback, then we will also do that with BBQ.

Should I involve the building surveyor before signing the contract so that he can review the planning documents?

Our construction expert has proven to be worth the money for us. Many craftsmen on the construction site said, "I know, this is being inspected." And the general contractor told us, done right and approved once is cheaper than doing it wrong and having to redo it. The general contractor was usually present at the inspections, and the two discussed matters objectively; we as laypeople were just amazed. Afterwards, the house was praised from both sides, and we would never have noticed the areas that needed rework.

I come clean, we built without a [Bausparvertrag]. My reasoning was: - I trust the site manager. He found and had several "errors" corrected on his own initiative. He also knew the problem areas during construction and paid close attention there – the [Bausparvertrag] looks "generally" - the [Bausparvertrag] is on the construction site 2-4 times. Ours was a prefab house; in the meantime, so much happens that the [Bausparvertrag] can't really check anymore. With brick-by-brick construction, it might look different because the house is being built on site - I was on the construction site daily and had my own eyes – what I didn't understand, the craftsmen calmly explained to me - I have 5 years warranty. What didn't catch my attention within that time is not a "defect" either