Current providers of cellular service to aircraft claim they will migrate to LTE for future delivery of data in flight.  Here an article debunks that notion.  It will always be limited.

LTE top speed is 12 Mbps

The reason is that LTE requires dedicated spectrum.  That means users of LTE will have to pay for spectrum at a cost now of billions of dollars to be able to use LTE.

Even IF they could get the data rates suggested below (which are point-to-point, NOT to a moving aircraft), they do not have enough dedicated spectrum to do it.  And when they switch to unlicensed spectrum as Wi-sky Inflight Inc. are doing, they will conflict with their patents and know-how.