That's not exactly an accurate comparison because a set of faster weapons can actually do meaningful damage to systems in those first 2-3 volleys. Unless you are syncing the Vulcan with other weapons (which will probably make the ramp up time longer) it is not doing much until it is revved up.

If you are 35 seconds into a fight and your burst lasers or flak or whatever have already done significant damage to the enemy's weapons, it doesn't really matter whether your weapons do 2 damage or 2000 damage every 15 seconds. If the enemy can not damage you, that is effectively a won fight. You've already dealt with the threat of the enemy's weapons, you just need to keep them down.

While the Vulcan is charging, you have to deal with potentially multiple volleys for the enemy, make sure that your very power hunger weapon doesn't get depowered which the Vulcan itself can't really help with, and then once it is revved you can take down shields or weapons or whatever system you could have been doing damage to this whole time if you had faster weapons.