2-3 tiles seems reasonable to me. I do think it's nicer to have a disease mechanic than just forcing them to be planted further apart, but this could also have a lot of bad effects if it's not done right.
If the required spacing is too large, it will just lead to even worse base aesthetics and the claiming of even more land that wouldn't otherwise be needed. I will want around the same amount of fruit as i've been getting before the recent patch and will expand the space of my orchard if I need to, i expect it would be the same for a lot of people.
my main concern is that having it apply even to trees out in the wilderness would be really bad, it would suck to have the world be mostly bare of trees in so many ways. i don't think people's regular tree forests for timberpiles etc are such an issue its worth an effect like that. How about leaving the regular trees alone?
having it apply to regular trees would also make it annoying to just use them for decoration and convenience around the base, like those trees by the ovens we all have. I'd also like to know if we can do something to cure a diseased tree. I think that would be important with fruit tree purity and continuing to have decorative trees and oven trees etc without it being a huge nuissance. If some portion of my trees will be dying each season, I might make an even larger orchard just so there should remain a reasonable amount of trees with decent purity. If i can cure my sick trees, I may opt for a smaller orchard I find it reasonable to maintain nicely.