If 98% valid test equates to a 1 in 50 chance of a false positive test, then that's another barrier to flying. That's a 10% chance of one of a family of five getting a false positive, or two crying families at the departure gates of every flight.
What would increase numbers flying, is guarantees of quick refunds on cancelled flights, and actual help getting flights home after cancellation. Also consistent and safe procedures on boarding and disembarking.