There's another train of thought on that. Instead of sticking to the path go well around it, therefore spreading the footprint over a wider area so it's not falling on the same spot.
Another major cause for erosion are mountain bikes. I've noticed this on Dartmoor, When i started walking it 50 years ago it was fine. Paths that had been walked for centuries were still intact. Now in parts they're chewed up, and the tyre marks are there to be seen. I'm not against bikes being used on the moor, just riders to use some sense when riding on a grass surface as opposed to a gritted rocky path. All the weight of the body and pressure of pedalling the bike, plus all the gear is being transferred through the tyres. Instead of going through puddles/soft ground, go around it giving the grass a chance to recover. I give muddy spots as wide a berth as I can. The exception to that is if I'm on boggy ground and there's no easy way round it. Then it's a case of ploutering on till I'm through it. So far I've succeeded.