NEW FLASH: Not everyone does.
This can occur in any kind of roleplaying game but it’s more common in larger games like LARPs where you can have dozens, even hundreds, of people all playing alongside and against one another. No matter how grand and powerful and scary the plotline you create, everyone is going to have a different level of investment in the outcome. And that level of investment can be 0.
So how can you keep an eye on the investment factor?
In larger games, you’re probably going to have to do a survey or some such because it’s really hard to get an accurate read on things when you’ve barely met all the players and don’t know their character arcs. You’ll probably have to look at each faction’s investment in the plot and work from them. In smaller games of 30 or less you can get somewhat of a gauge by sitting down and thinking it through.
Has the person never encountered an NPC related to the plot line, have no personal ties to the plot line and is their character unlikely to be able to interact on a meaningful level with the plot line? Probably not heaps invested then unless they, as a player, find the plot line super interesting and in that case you should probably throw them a hook so they can get involved.
Of course, even if you can tick YES to those boxes it doesn’t mean they care. Practically everyone can remember a tabletop game when a plotline came up that they just weren’t that into. This could be that they, as a player, just aren’t particularly hooked by it or it could be that the execution hasn’t been that great or it could just be that they need more time.
The thing about investment is that it is a slow and gentle process. Rush it, or worse – demand it, and you’ll actually lose it. Give them reasons to care but accept that it’s a valid response to either not care or to care for unexpected reasons (such as wanting their country to fail rather than succeed). Or it could simply be that there are too many people involved in that plot thread already so it would be difficult to have a meaningful contribution without pulling it away from someone else.
This is why it’s important to have several plot threads, especially in larger games, so that everyone can be involved in something even if they can’t be involved in all things.