Why does it seem like the Sole Survivor is the only minuteman that can go to the aid of settlements under attack? For that matter why can't well defend settlements handle it themselves?
Perfectly valid questions in my mind.
So I'm suggesting two different mods to address this.
1. Dispatch help. Once you're in a position of authority you should be able to delegate. Settlement A under attack? Order minutemen from either the nearest allied settlement or some from HQ to go sort it out. You have other things to do. There could be a version where this option only exists if you have already completed the given quest once yourself.
2. Timed mission. After a set amount of time the settlement will either A.) Succesfully deal with it or B.) get wiped out. Base it on the defense value and number of settlers vs. the level of the threat. Probably a good idea to list that threat level (or probablity of settlement success) in the quest discription.
These tow ideas could also be used together.
For those who want more depth you could also give the minutemen a reputaion value. Increase when a settlement gets help, no change or minor decrease if the settlement handles it on their own, major drop if the settlement gets wiped out.