We have peach trees coming up all over, planted by squirrels. I had a freestone I grew from seed and a Cherokee White. Not as good tasting but had an edible pit. They cross pollinated, and crossed with offspring first and second generation so had all variations. All were excellent tasting. We do not spray chemicals but we do spray aerated
compost tea with trace minerals, humate, worm castings and extra cal/Phos in it. Spray all over the trunk, ground to 2 feet beyond drip line and leaves on the tree. Never have worms. But weather here is iffy and late spring frosts usually take them out or too much rain at time to ripen makes them rot. Always get a few really good ones, usually soft ball sized. Sometimes they start bearing at two years old, just a few blossoms, especially if I put a few cups of kelp sprinkled around under the tree. They grow insanely fast, short lived. Keep center pruned so it is open and has good ventilation. Our trees are pretty much neglected and do well.
With appropriate microbes, minerals and organic matter, there is no need for pesticides or herbicides.