Each consistency check should be time-controlled and executed 'atomically' (i.e. splitting a check that runs over n objects into n checks, each of which processes only exactly one object) via the Job Queue in the background, and its results should be written to a newly defined table.
Each consistency check should be assigned to a schedule: Important consistency checks should be triggered more frequently (weekly?), less important ones monthly.
There are also checks that should not be triggered automatically.
An enhancement request (#32257) has been created.
The product team will evaluate the request and this feature may become available in a future release of the product.