It seems to me that it was possible to destroy them with a cheaper way. To achieve their goals in Syria, the Americans need to destroy the most modern weapons, and then old. Maybe the goal was the other?
By cheaper way, do you mean dropping bombs from military jets? It is definitely an inexpensive option, but there is always a risk of one of these jets getting shot down, and the pilot being taken as a prisoner of war (if not killed). If something like that happens, then Trump can kiss his popularity ratings a good-bye. They will nosedive from the current 35% - 45% levels to single digits.
There is another way. To put opozitsioneram portable anti-aircraft missiles to the rebels could shoot down planes and those from the earth very quickly destroy all airbases of Syria, and Russian.