I've travelled through airports being disabled, though not in recent years.
From my understanding its the individual airlines that carry out the helping of disabled passengers, not the airport itself. I could be wrong though. I know the airlines do at least part of it as I've had experiences were the airlines have gone the extra mile, while others who messed it up totally.
On the Dover situation. From my observations of this, the UK government needs to either come to some immigration agreement with France (and maybe Spain) were they agree a version of free movement so that the immigration people only need to identify your British, French or Spanish and wave you through, like what used to happen. If that kind of deal is possible to be done then make it a template for other countries too. If that can't be done then the French are talking about UK joining the Schengen agreement, which would have the same effect. I'm not sure what restrictions can be applied during that agreement. From next year the EU will be making everyone outside of the EU have to apply for a Schengen electronic waiver.
1. Other non-EU countries are involved in Schengen, 2. Next year UK people will have to apply for an ETIAS (European Travel Information and Authorisation System) electronic waiver, which is replacing the physical Schengen visa (at the moment we dont need a visa or waiver. But we will when ETIAS starts in 2023). 3. As if all this chaos isn't enough the UK is introducing its own ETA (Electronic Travel Authorisation) waiver, which will be trialed from 2023 to a few countries around the world, then by 2025 will be brought in for most other countries, including the EU. So we're going to have a double whammy. I think it would be better for the EU ETIAS and the UK ETA systems to merge, if not for the pure fact that currently both systems won't be able to access each others data. If they merged then we'd be able to share traveller information, and of course we'd have less delays.