ycbm
Overwhelmed
to a point yes but if walking a lame horse just makes it move even more badly then it usually has a knock on effect to somewhere else in it's body. Depends whether that potential further damage is an acceptable risk or will make matters worse.
The ideal is letting it wander without a human demanding a walk or a herd to bully it.
It's not ideal if it doesn't cure it. I've had one here that was lame for four years including several spells of field rest, the last one a whole year. Horse was still lame. I walked it and walked it and it was sound within three months. For me, that's also the point of a flat road. They move with least effort on a flat hard surface and don't do themselves further damage elsewhere. You can't stop the damage til you get a heel first landing. You can't get a heel first landing if you don't strengthen the heel. It's not chicken and egg, the heel and foot balance has to come first or the damage never stops. Rooney's experiments showed this clearly.
I'm not sure where you get the idea that rehab horses move because the herd bullies it? The rehabs I've had have followed the lead horse, not been pushed by it.