That makes technical sense. Original Iridium uses weird modulation scheme (which is also used as security-by-obscurity) for the sole purpose of having simple ground terminals, while Inmarsat in it's current generation is "bounce UMTS off GEO satelite" which requires either stationary or surprisingly complex ground terminals.

SpaceX's network seems to work the other way around by being designed around fast-moving satellites and complex ground terminals that do the tracking and hand-overs by means of phase array antennas (ie. completely solid-state). In comparison to Inmarsat it is not GEO-bounce and in comparison to Iridium they seem to have some solution for having fully connected mesh of satellites (original Iridium is not fully connected sphere as there isn't even attempt to have link between satellites with oposite orbits)

Antenna as big as a pizza box. I believe I heard mentions of using it on cars (Teslas?) and other moving vehicles, like boats.

Mobile uses (including cars) are only speculation at this point. License is for fixed, and only references have been to fixed.