Please explain this. Isn’t dispersion/directivity a function of the enclosure and how sound radiates from the drivers in concert with the enclosure? How does flattening the FR change dispersion? So many folks have said here in various discussions that EQing for FR is pointless with an enclosure that gives poor dispersion. This suggests that they are not related. Thanks.
You are correct that a driver's directivity is is determined by things like its dimensions, shape, interactions with array members, and its transition to the space it radiates into via a baffle or horn. However, overall system directivity is the sum of all these drivers, and a crossover can blend the drivers' directivity more or less, over a narrower or wider bandwidth.
Steep crossover slopes can make directivity transitions more abrupt, which is not a problem if drivers are well matched. If you have drivers of very different size, like a 1 inch tweeter and 7 inch woofer, a shallower crossover is generally advisable. A four way speaker has smaller differences in directivity and it is generally better to have steeper crossover slopes there.
A common mistake in crossover design is to use steep crossover slopes to reduce distortion, sacrificing off axis response. This is a mistake because distortion is generally inaudible, but off axis tonality is not. This error is common because measuring distortion is much less time consuming than measuring dispersion.