A succesful gene drive to eliminate the asian hornet might be an option if the numbers of injuries or fatalities increases to a level where normal day to day living becomes risky.
Ie for example forestry workers, farmers even gardeners or beekeepers.
It is a non native species after all.
There is a gene drive underway in South America to try to control the Asian tiger mosquito (non native to south america), a vector for some of the most dangerous viruses that exist, one being Dengue Fever. I contracted this some years ago and it was truely awful and to be completely honest I've never been the same since, health wise.
So given my experience with Dengue, I'd be in favour of a gene drive to control asian hornets.