Surface to surface missiles are basically just indirect fire. I believe that the Army's MLRSs would qualify for IDF.
The difference between IDF and direct fire is mostly to reduce collateral damage. Direct fire can be more accurate and limit damage to surrounding areas. It is also easier to hit moving targets with direct fire.
I don't know all that much about what weapons the US currently uses on the battlefield, but I'd imagine that missiles laser-guided by ground troops would be accurate enough? Also, wouldn't CAS be better handled by UAVs anyway? They're cheaper, they have much better payload-to-weight ratio, and don't put a trained pilot in harm's way.
I think UAVs are great but not everyone is Type 1 CAS qualified. Someone could correct me but I think most UAV strikes are Type 2 or 3. A Type 1 CAS has to visually confirm the location of the target, friendly, and the approach angle. Most pilots, SF, and a lot of ground troops are but not all. And they are often not in a position to be able to confirm everything. Calling in CAS is a great responsibility in that you are accountable for every bomb or missile dropped.
The difference between IDF and direct fire is mostly to reduce collateral damage. Direct fire can be more accurate and limit damage to surrounding areas. It is also easier to hit moving targets with direct fire.