You are assuming one needs to get up close and personal to provide CAS. That used to be true, but is not any longer. With modern targeting pods, it is possible to provide more accurate CAS from 30K than from 500 feet.
Not my assumption. My assumption is that you need to be able to loiter for long periods of time and that the more ordnance that you can haul the better. Aircraft designed to be fighters have the wrong type of engine (low-bypass) and wing loading for this. Thus, they are not optimized for CAS.
But getting lower than 30k feet can be very important in CAS. I've tried to pick up targets to bomb from 20k and its not that easy. If GPS isn't available, then CAS must be talked onto the target using identifiable landmarks. Those aren't easy to discern five miles up or at 600 kts down low.
The answer to that, flying lower and slower then requires the ability to absorb some punishment.
Now if you are confident that you can always provide CAS from 30k feet and that survivability isn't an issue, I recommend installing bombays in Boeing airliners. They are better suited for range, endurance and load-out than F-16's.
It was a shame that during the Korean war P-51's were sent to provide ground support and all the surplus P-47's sat in the Desert. The P-51's were far more susceptable to ground fire and suffered accordingly.