From the FP+ Roadmap: ~68% of guests in the MK used the paper FP system (about 31.9K of 46.7K daily attendance, 2008 stats).
Disney said in 2014 FP+ was up 40% from that, so that would mean 95% of guests were using FP+.
I have some doubts about a claim of 95% in 2014. For one thing,
only 64% of Americans owned a smartphone in 2014 (it's ~78% now). But even if it's 20-30%, that's still a big increase.
But those figures could also be very misleading.
What I mean is, how many of those that Disney say are “using FP+” are actually using it to book FPs in advance?
This is purely anecdotal, but I estimate only around 10%, maybe 20% at best of first time U.K. visitors use it before they visit. The vast majority stay offsite. They’re booking villas or a cheaper hotel somewhere. Even if they look at the Disney website, they could easily miss the whole FP+, until they arrive at the park. For a start, they don’t plan out when they’re visiting WDW, or Universal, or Bush Gardens, or Sea World. They have 2 or 3 weeks and tickets that are good for any time, so why worry?
I work in a primary school of around 450 kids. Each year I reckon around 30-40 families head off to Florida, maybe half for the first time. And each August and September, when I talk to them about what they did, most of them didn’t get to do all the rides they wanted. “The lines were too long. We didn’t get those passes to jump the queue, like at Universal”. I bet a lot of them only really realise how to use the system once they’re there for their first day. Then they’ll see what they can book for later when they return to visit AK, or Epcot etc. They’ll still be included in that figure of visitors using FP+, as will anyone only using the kiosks.
In some ways, it’s easier for them to just buy front-of-line passes at Universal when they get there.