World of Warcraft lets you pause duty finder queues. You can pause an active duty queue simply by entering the Proving Grounds. Not only that, but it also allows you to chain-queue multiple duties simultaneously, such that if one pops and you enter, all other queues are paused until you complete the current one. For example you can chain-queue all 3 wings of LFR Battle of Dazar'alor simultaneously. When one of them pops, the others will be paused. When you complete the duty, the others will be immediately unpaused, and the next one will typically pop very quickly. It's not uncommon for the next duty queue to pop within seconds of the the current duty's final boss dying.

I would like it if FF14 were to add a feature like that.