My thinking of the reason it isn't usually done is that horns are generally used over the bandwidth of the horn, and not as direct radiators below the horn's cutoff. There are some exceptions though.The problems are that the horn tends to get peaky down low, and that output below cutoff will be reduced, forming a shelved response. But if the horn is very oversized or used in eighth space, the response down low is less peaky so that can be a solution. As for the shelved response, you gotta deal with that using some form of EQ.
One can always use a subwoofer and crossover to the horn above cutoff. That's the traditional way. But another solution is to run the driver below cutoff as a direct radiator, using either as a sealed or vented system.