Not many people have a yard the size of half a football field, and even if they did, it would probably put the danger close to a neighbors house.
So seriously, what would a reasonably safe distance be? Should this be avoided if you don't live in a really rural area with a giant property?
It's not even so much the DIY aspect of this that's an issue, as much as it is people thinking it's OK to use old batteries. It's not. These are not deep cycle lead acid batteries. LiPo cells have a very definite cycle lifetime, beyond which their internal resistance grows to dangerous levels. Using them beyond that is just reckless and irresponsible.
I haven't done enough research to feel comfortable giving a number, but it should be well under 50ft even.
You do make a good point that this won't be an option for everyone. If you live in a dense city without yards, I guess this is one fun project I'd take a pass on. If you live in a standard suburb you are probably okay at least in terms of space.
Here is a decent primer. At about 26:30 they talk about battery failure testing. They have a 2 ton blast door in the room where tests are conducted.