Full frame sensors cost about 10x what an APS-C-sized sensor of the same generation costs (
Canon has a white paper explaining that in detail, look at Section IV). And since most of that is attributable to geometry (an 8" wafer fits 20 full frame sensors but about 200 APS-C-sized sensors, but then there is also the problem of yield), the difference won't decrease significantly.
So I don't think full frame sensors will replace APS-C-sized sensors for the bulk of the market. There are full frame sensor-based mirrorless cameras available right now (e. g. Sony's A7, Leica's M and Sony's RX1), but these are sitting right where full frame dslrs are, at the top end. And don't forget that also other components and lenses for full frame sensors are bigger and more expensive.
Full frame sensors are already the present, but they will never become the sensor size of choice for the bulk of the market of mirrorless cameras and dslrs.
So does the RX1. But the A7 costs $1500 and you need to plunk down $2800 for the RX1. Similarly equipped cameras with smaller sensors are significantly cheaper (e. g. Fuji's X100s costs $1300, Nikon's Coolpix A is end-of-life, so it is on sale for $1100 -- both cost less than half of the RX1).
Bingo. Full frame sensors and medium format cameras won't go away, but they will never become main stream -- if only because of the price alone. I'm glad my mirrorless camera doesn't have a full frame sensor, because otherwise, I wouldn't have been able to afford it