I still think we're very early in the FP+ rollout. There's nothing intrinsic in the FP+ system that say 3 FP+ is a limit. As has already been mentioned, Disney is in the process of allowing guests to park hop with FP+, and is allowing additional FP+ after the first three have been used - and we're only a few months into the new rollout.
If you think about it, if the FP+ is a success, then why would Disney want to restrict its success to a 3-hour window (or 3 separate hours) when the FP+ is available to you. If it's truly a better system (i.e. making money for Disney), then they would want you to use FP+ for your whole day, and your entire WDW stay.
Basically (and I've written the same thing in other threads, so I apologize if anyone is reading this twice), FP+ will work when guests have time to "stand around" between rides. They are more likely to use that time to shop, eat, etc. This is where Disney will make their money.
In other words, if you just got off one ride and it's still an hour or two until your next FP+, you're not going to wander aimlessly about the park, you're going to go standby for another ride.
However, if your next FP+ is only 30 minutes away, and you've planned your FP+ for the rides to be near each other, then you have 30 minutes to kill before your window opens up. That's probably not enough time to ride another standby line, so you're likely to just wander around, look in the shops, get a bite to eat, or whatever. In other words, spend money.
Disney's goal is to give people as many of these "shopping windows" as they can. So, they start with 3 FP+, and see how it goes. With Magic Bands, they can actually track where you were and what you did in that window, too - since they know what ride you were on, and what ride you went to next, they can probably figure out you exact path from one ride to the next - especially if you make stops along the way. They can tell whether you went left or right, and which shops/restaurants along the way actually earned your money. They can change a store display, offer a special, or waft a new smell in your direction, and that same day they can calculate how many shoppers it attracted.
They can save money with it too. Before, you never really knew how long the lines were going to be for any particular ride, because it depended on the whim of the guest. If it's planned out, Disney will know exactly who will be where, and when. They can move personnel around, add or delete cars or boats from an attraction, or whatever they need to do to cut costs and increase guest satisfaction.
The possibilities are nearly endless.