Alright well seeing as how I frequent these forums, I can answer this myself.
Delicious trees, when overgrown will have a higher likelihood to become "naked trees", meaning that when you shake them they will lose all their ability to grow new fruit and any leaves on the tree (hence becoming "naked)". Basically the tree becomes useless after that. Not only that, but they will leave behind a rotten or bug-infested fruit. This costs money to throw away so the best thing to do is just chuck it in the trash.
The more of these trees you have, the more likely it is to get the phenomenon known as naked trees. There is no X amount that you need to pass. Just like basically everything in this game it has to do with balance. I've noticed that certain spots are more apt to become naked trees, and if I have grown way too many I find they will become naked a lot more often. If you just keep a few or even a fair amount around you'll probably not run into this too much.
Again, this is all just from my point of view. During a time when I only had about 5 delicious trees, every time I shook them they were pretty much fine. As soon as I had about 40 and began shaking they basically all became naked (over 25, easily). This, to me at least meant that the more you had the higher the chance (perhaps because the balance is off, wherever that mark is I do not know though). It is a little misleading to assume that it is ALWAYS random because from my experience, when I had >10 it almost never happened. Sorry if this is confusing...just my findings
Also for those curious, I tackle this question way back in video 23, start talking about it around the 5 minute mark (
https://www.youtube.com/watch?v=85yr3yTTcc0).
I just find it weird that the Delicious Oranges have a different shape in the first place. Delicious Peaches have the same shape, just a different color. Why aren't Delicious Oranges just a darker shade or orange or something?
They look just like Dekopon from my perspective. They are kind of like an orange, really common here in Kyushu where I live.
