I have been experimenting with this. . . .
The old adage was the untrimmed feet caused foot problems, whereas now it seems more likely that foot problems cause overgrown feet (due to less pressure being placed upon them).
Trimming bad feet seems to prolong the time it takes it to heal. In one study, they trimmed one batch and jabbed them, and didn't trim another (but also jabbed them), something like 90% of the untrimmed sheep were sorted within 5 days, but less than 50% of the trimmed feet.
However, to be honest, repeated exposure to a/bs is a bad idea, so the best idea is to try to breed it out. A predisposition for foot root is a genetic trait, so although you will always get some sheep with it, with decent recording and culling you can seriously reduce the levels of F/R in your flock.