In the end, for a commander, it comes down to a balance between gear and man.
A crossbow is an equalizer, in that even a poorly trained troop can use it. . .but it's expensive.
A longbow is a multiplier, it takes the right person, with the right training, to use it properly.
Often, the crossbow costs less then training and maintaining longbowmen. . .so in history, it's often better to have 5 crossbowmen than 1 longbowman. (You'll notice the major difference, that the crossbow dominated armies were ones where a rich guy provided poor guys with crossbows, while the longbow dominated armies were made of yeomen, who provided themselves with a longbow.). . .many cultures wouldn't sit well with the idea of a whole class of people running around loose with heavy ranged weapons all the time, just so you could call up your longbowmen when you needed them. The lifetime training a longbow master needed created a class below the nobility that had greater political rights, simply because there was an armed, non noble class running around. The continental cultures did have some similar examples, not all longbow based, like German Jaegers, but it wasn't a widespread phenomena, for a lot of reasons, mostly political and economic.
The ROF issue essentially only matters if you have time. . .if two ships close and boarding ensues, the benefits of a crossbow to fire once, dump, draw and board are good enough. . . .in an open field battle where the longbowmen are covered by infantry from charges, the ROF benefit tends to come to the fore.
I never said crossbows were bleh. . .just that thrice dead is not much of an improvement over dead. . .and once you get a weapon deadly, it's better to get the ROF up than to make it punch harder. Hence the switch from 7.62mm single shot rifles to 5.56mm assault rifles. Of course, that example turns the previous logic on it's head. . .since single shot rifles benefit skilled operators more, while auto rifles benefit noobs more.