One thing that has to be kept in mind, however, is that even if the plane is fitted with the necessary hardware that doesn't necessarily mean that connectivity will be available throughout the flight. The link here shows Inmarsat (now Viasat) FX coverage. A lot of the polar regions aren't covered and those are where a great deal of transatlantic flights go.

Another issue is beams saturation, especially in SE Asia (from Singapore to the South to Shanghai to the North).

Eventually, these problems will be solved through the cooperation of LEO and geostationary constellations, but that's a few years away.