Chainring wear has little to do with downshift performance. The FD typically moves in via the return spring, so slow downshifting might be the result of cable friction, or poor FD adjustment. It might also be the result of your not easing up on the pedals to allow the shift.

Shifting requires the chain to lift over the tops of the teeth. High chain tension from pedal load, resists that by pulling the chain down onto each tooth as it engages. So the very first step in dealing with sluggish FD shifting is to check it at zero load. If it's still sluggish, then cables or adjustment.