The products and installations are subject to certain standards, so it can be assumed that, if installed properly, approval poses no problem at all.
You got it, that’s exactly the point! This is precisely what my brainstorm aims at, as well as an optimized, well-thought-out location for the outdoor unit. By the way, the legislator initiated these "certain standards" with its 1st BImSchV. The question is why air-to-water heat pumps are not also subject to a "certain standard."
So one should just set up an air-to-water heat pump
Hopefully no one just installs an air-to-water heat pump like that. It needs to be properly planned—both from a heating and noise technical perspective.
...to realize upon approval...
The noise measurement on the actual object afterwards is also purely formal following the compatibility verification made during approval. Just like with gas, oil, and pellet heating systems, it is purely a determination of the source emissions, not an immission measurement at the neighbor’s property; specific conditions on the sound propagation path as well as the source and receiver environment are already considered in the theoretical verification. And no, this is no witchcraft, but carried out via situation-related surcharges; we are still talking about a point noise source here. The heat pump noise calculator of the Federal Heat Pump Association already does this very well (by the way, based on the LAI sheet); the weak point almost always lies with the randomly assigned sound power levels used by the manufacturers for the systems.
then what to do? Tear down the heat pump?
Back to small combustion installations: What happens if your oil, gas, or pellet heating system does not meet the limit values of the 1st BImSchV during commissioning or a recurring inspection?
incredibly many variables
No. These uncertainties are already eliminated in the compatibility verification during the approval process, ideally before that in the planning process.
It is therefore completely unclear before installation whether approval is possible.
See the verification in the approval process.
Likewise, a regular check, as with gas boilers, is not necessary, since there is no (life) danger arising from lack of maintenance.
There was and is no talk of operational safety regulations. The 1st BImSchV deals with air pollution control and energy efficiency.
Incidentally, there is no need to subject something to inspection generally just because it presents a problem in a few cases. Absolutely the wrong (uneconomical) approach. You might as well get a stamp from the authorities confirming you tied your shoes correctly.
Following this argument, TÜV (technical inspection) for cars as well as any other recurring technical inspection would be obsolete. "Few cases" (though my professional experience differs) are inevitably the result of recurring technical inspections and therefore an indicator of their elemental importance, not their redundancy.