I was lucky enough to be part of Lew Pulsipher's AD&D gaming group back in the mid-'80's to early '90's while I was stationed at Ft. Bragg. Being the quintessential game theorist, Lew really helped me broaden my play and my DMing.
Because of the number of people participating in Lew's campaign and because several were soldiers, like me, Lew had an approach I think of as 'jazz band adventuring'; instead of a set party (Joe plays the fighter, Lisa the mage, Frank the thief, etc.) Lew would announce the level of play and what our characters generally knew about the adventure and we would make an adventuring party based on that. While the party would stick together for that adventure or arc, the next adventure arc could have a completely different 'band'. Also, since some players might not be available we needed a number of characters per player ready to go.
The result, which I replicated in my own campaign of the time, was that each player tended to have 3-5 characters that 'lived in' the same campaign city and interacted all the time. This led to a very dynamic campaign (you could easily have an adventure for 9th level characters for 1-3 sessions then follow it up with a 2nd level dungeon crawl with the very same players one session later) with a lot of player-driven background action - the stuff in the campaign world not directly part of a particular session, like castle building.
For example, I had a large number of characters in the game (no, this will not descend into 'let me tell you about my 12th level paladin', I promise): a 2nd/3rd illusionist thief, a 5th level magic-user, a 5th level cleric, a 6th/6th elven cleric/magic-user, a 7th level paladin, then a 14th level paladin and a 14th level magic-user (the highest level characters in the campaign at the time). Considering that within the 1e campaigns we were both running 9th was considered 'high level', this means I was ready for most adventures.
Here's an example of how it would work; The DM for the next session would announce the level and general outline of the adventure coming up ('you are going up against the plague priests of the Briars, about 5th level'); We talk among ourselves and show up with Jen's 5th level fighter, John's 6th level thief, Amy's 3rd/3rd fighter/cleric, my 5th level magic-user, and Keith's 4th level ranger. At the end of the session, we are still deep in the Briars, so the party stays the same for the second session. At the end of the 2nd session the party makes it back to the city with the ranger's body in a bag of holding and the thief suffering from the Crimson Plague (courtesy of a Cause Disease). At this point we 'put out the word' and for the 3rd session it is Keith's 6th level thief, John's 5th level magic-user, my 5th level cleric, Jen's 5th level fighter, and Amy's 3rd/3rd fighter/cleric. Not because the ranger was still dead (the character was raised) or because the thief was still sick (she paid for a cure), but because the original party wasn't working the way we liked - like a jazz ensemble, we mixed things up a bit.
I certainly understand how having the same party as a coherent group works - I have been running the same players with the same characters in a campaign for the last 3 years - but if you have players interested in it jazz band adventuring can add a lot of flexibility to the campaign. Want to introduce an important NPC or plot point, but it makes no sense for a group of 9th level characters with strongholds to meet them directly? Have them encounter a group of 3rd level adventurers, instead. Feel as if your players are treating their henchmen like emotionless drones with no back story? Have them play their henchmen. Better yet, have them play someone else's henchman - they won't treat their NPCs like meat shields any more.
There is another benefit in jazz adventuring for some DMs. Do you avoid situations where a character might die because it will derail the entire arc? Well, in jazz adventuring each character is just as important, but not are too critical - even a TPK doesn't derail arcs,
"Father Blaise! Father Blaise!"
"Yes, my child?"
"Baron Eric, the Archbishop, and their companions have yet to return from Mount Doom. What are we to do?"
"Tell Sir John and his men to meet me at the church. I may not be the Archbishop, but I am sure we can rescue them!"
When there are other characters that can immediately step in for everything from rescues to continuing the mission it allows you to keep the possibility of capture, death, or worse on the table (pardon the pun). Knowing this, it makes the tension much more real to the players, too.