For idle games, much of the point is investing in auto-building, then coming back to the game when your investment has borne fruit. For this to work, it has to be able to run in the background.
There is a big difference between throttling and not running. Still, it is probably much better to sync with the server than run something at full blast to increment some counters.
Sounds like it's time for the game authors to provide some servers with the compute resources to do this background processing.