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.