The exercise selection criteria of moving the most weight over the most effective range of motion using the most muscle mass inherently includes "and doing so safely", since causing injury precludes effective strength adaptation.
The low bar squat is already optimized for these criteria. If it's already optimized for safety and effectiveness, how would introducing instability help avoid further injury?
And single-leg vs. double-leg is definitely less stable, no matter what The Karate Kid would have you believe. (Even there, remember that Daniel-san didn't remain standing when he tried to land on the injured knee.)