I feel there is a difference between
There's a fence to stop people from walking on the grass.
People are not walking on the grass now, and the fence is there to make sure they won't do it either.
I would probably phrase this as:
There's a fence to keep people from walking on the grass.
It seems more logical to use
stop as I presume the fence was not put there while people were walking on the grass.
That would lead to an interesting situation without
There's a fence to keep people walking on the grass.
In which case, obviously, I have locked people up, and I want them to keep walking on the grass (and possibly sell tickets to people that want to see them).
There's a fence to stop people walking on the grass.
It is people's habit to walk on the grass, that is bad for the grass, so I put up a fence to stop them.
So, I agree that on one hand stop ... from and simply stop convey more or less the same meaning and from is in that particular case optional.
I also agree that the version with
from sounds a bit off, and I'd prefer the version without.
from, I would use a different verb (
keep), and then all of a sudden
from is no longer optional!