Probably true for a 3 way, but in a 2 way with a larger woofer if you cross a large woofer over too high, it will start beaming. If you want a more full sounding 2 way with a bigger woofer and not trade off imaging and soundstage (with a 2-way, this tradeoff basically exists with anything bigger than a 5"), you will want a highly capable tweeter that you can cross over lower.
If a designer can do so with the driver on hand, they will. Look at the Revel M106 and Revel M126BE, designed by the same team. When they got their hands on a beryllium tweeter, what did they do? Drop the crossover frequency by 600 Hz in order to achieve much, much better dispersion characteristics. Of course to do so you need a much better tweeter with bigger magnets, stronger voice coils, and exotic diaphragms.
If a designer can do so with the driver on hand, they will. Look at the Revel M106 and Revel M126BE, designed by the same team. When they got their hands on a beryllium tweeter, what did they do? Drop the crossover frequency by 600 Hz in order to achieve much, much better dispersion characteristics. Of course to do so you need a much better tweeter with bigger magnets, stronger voice coils, and exotic diaphragms.