I just looked at a small site with a terrible mobile experience that was flagged by Google as mobile unfriendly.
April 1 - July 31 this year is up 50% in mobile sessions coming from organic search while overall it is up only 28% (most of which is due to mobile)
On the other hand, mobile sessions coming from direct and referral are up closer to 90%, while overall they are much lower.
So it's not like the site got banned, but mobile organic is up much less mobile from other sources.