//...why so terrified of processing them inshore? Scared they'll catch Covid?//
Because once they are "inshore" the likelihood of them being removed, even if their claim for sanctuary is patently absurd, is vanishingly small.
Poland has adopted the correct approach to the problem they have on their border with Belarus and it seems to have borne fruit
https://www.msn.com/en-gb/news/world/belarus-has-lost-the-battle-on-border-after-migrants-given-shelter-in-factories/ar-AAQOcvE?ocid=msedgntp
The invasion currently being suffered in Kent is every bit as illegal as the attempts being made to get into Poland. The only way the rubber boats will stop crossing the Channel is to stop ferrying the occupants into Dover as soon as they cross into UK waters and, for those that do make it unaided, make life as extremely difficult and unpleasant as possible. So long as they are welcomed with blankets, food, hot drinks, almost immediate accommodation and money it will continue.
Illegal migrants living in France are not in danger, they are no facing persecution, they are not facing death. They simply don't like it where they are and that's not what the asylum system was designed to address.