BasicMed still requires a physical and that's a higher standard than nothing.You already don't need a medical to fly s 172. They're not falling out of the sky.
Time will tell. One prominent LSA crash and Sully's congressional testimony is all it would take for the policy to be revisited.
I'm not encouraging such a change and don't think it's warranted but struggle to ignore my observations.
Years ago we all flew overweight ultralights and nobody cared. Even today, there's been no crackdown on two-seat (former) ultralights that continue to be flown.