The form itself is usually a small part of the cost of a slow permit, since the bigger cost is the crew waiting to start work while the permit moves through approvals. Measuring the time from permit request to work starting, multiplied by the size of the crew waiting, gives a much more realistic number for lost wrench time.
There is also value in fewer permit errors, fewer conflicts between jobs and a cleaner audit trail, which are harder to put a number on but matter a lot to safety and compliance teams. A good business case includes the waiting time as the main number and these benefits alongside it.