Starlink user terminal is "physically" not designed for working in motion. That is, it has not passed any safety tests that ensures it won't dismount, and fly off and damage property or injure people. The Starlink system is absolutely designed to work at high speeds (both as evident from comments in this post from people maintaining connection at 100km/h to it being deployed on airplanes).

There's also the physical tests of the motors being able to withstand the wind force loading.

And no it's not designed to work at high speeds. People keep confusing "designed to work at" with "possible to use outside of recommended conditions".

The system being deployed on airplanes is somewhat different than the one being sold to consumers.

From the horse's mouth: https://twitter.com/elonmusk/status/1529089543969943553

Work doesn't mean work correctly. And he also said that the warranty is void in such case. https://twitter.com/elonmusk/status/1528879210500132866