You can have better results potentially in rural areas because the lobes are usually set to a higher elevation and also use a higher power output for more range.

But the towers do actually intentionally filter out signals which have too much doppler shift, since modern cell systems use very tight frequency slices to accommodate max users within the allocated freq range. A jet flies fast enough to induce enough doppler shift to get rejected by the tower because it's infringing on other user's allocated slice. The tolerance for that was set specifically to allow enough doppler shift (and maybe also system frequency slop) to accommodate users in ground vehicle, but since jets travel significantly faster than ground vehicles they can easily exceed the allowable tolerance. Doppler depends on your direction of motion relative to the tower, so it is possible on the right heading to stay within the allowable doppler shift, and also stay within a lobe long enough to get useful service (perhaps to send a text or email, but probably not long enough to have a phone conversation).

You could hypothetical fly a circle around a tower at the right distance and altitude to stay within a high lobe with zero doppler. That should give you good service, probably even up in the flight levels.