I have to admit, I don't immediately have an idea for how to encourage players to buy into the logistical detail of expedition management as fun for its own sake if they're not already inclined to find such things entertaining, but maybe a minigame rules module might help?
This is a big challenge I've encountered int these kinds of games. One reason I've run them, is I have and have had players who find this kind of logistical stuff very entertaining. I've often come up with various systems for managing the logistics. I've found very few that don't get brushed to the side by such players (for example I've tried to abstract things like costs and hiring large groups, and most of these players want things concrete, not abstract: I pay 100 gold and get x).[/quote]
My post-apocalyptic game was a little different because the NPCs were being paid to stick with the PCs - they were there for survival. But I think the players generally reacted positively to having NPCs with positive attitudes towards them. After saving their lives once or twice, the NPCs were really grateful and helpful.
If the PCs are respected and looked up to, I think that makes a big difference in how the players regard the NPCs. In too many games, PCs don't get much respect from NPCs.
For bookkeeping - I maintained a columned sheet with the NPCs that were with the party at any time - it went into the middle of the table in a folder with other general info for them - including player maps and abbreviated character sheets for the NPCs who had some class ability. We just would collectively update that sheet as things changed.
I feel like it's pretty easy to discourage this just by having a bit of trouble to have the NPCs around - between bookkeeping and expense and morale problems, the players could easily find it not worth the effort.
One thing that comes up a lot in these games is sending out groups of hirelings to do things (assassins, builders, diplomats, etc). What I found worked well here was assigning a score that translated into a dice pool (my game is based on dice pools) of 1d10 to 6d10 (and there is a lower rating for unranked characters where they roll 2d10 and take the single lowest result). So the players might have a right hand man who has a general rank of 4d10 for the things he is sent out to. Or they might have a hit squad with a rank of 3d10. Anytime they send those characters do do something, I will roll that pool against the target and determine the result that way. This generally has worked well.
That goes even more broadly than having hirelings do things. If you're dealing with the larger scale, it often necessitates more abstraction. In my Vinland campaign, there would sometimes be mass combats as part of raids with many dozens of combatants, and I'd handle those as just having each player make three skill rolls on their most relevant skill, and narrated it as events over time.
I'd consider using a more mechanical mass combat system - but only if it is really well worked out and interesting to play. Just tossing in some arbitrary mechanics is worse than hand-waving it, in my experience.