While I personally would love to have the Priest in USF's Major Tier, I think that'd be a bit OP. USF's lone weakness really is its inability to break up enemy fortifications / fixed positions, and giving them access to the Priest every game obviously eliminates that weakness.
We don't want USF to become Allied OKW, good from 0:00:00 to Sync Error and able to hard counter anything Axis can throw at them. If you want long range indirect for USF, there's Tactical Support and Infantry Company, two very strong commanders that round out the core roster very well.
It's more than a weakness in my opinion, it's a handicap. The Priest in the core tech tree would be tied to a major, so it would be hard enough to get at its current fuel cost, and takes a while to pay off because of its accuracy, compared to the effect of the Katyusha or Panzerwerfer, which you can see immediately.