In our basketball league, we use a running clock (20 mins/half) in order to fit every game within a 1 hour slot. Since the clock is running, we too try to avoid having tons of clock eaten up at the free throw line. But since our culture likes shooting free throws, we let the shooter have 1 free throw that is worth either 2 or 3 points. If the shot was made during the foul, the +1 is added automatically without shooting a free throw.
We explain the reasoning behind it with the running clock to all the teams at the start of the season, and we haven't had any issues.