plants grown from seed don't bear the same fruit

Temperate-zone seed fruit like apples and pears rarely look, taste, and feel like their genetic parents.

Temperate-zone stone fruit, on the other hand - think peaches, apricots, cherries, etc. - are quite different. You plant one of those seeds, and it will bear fruit that is (usually) indistinguishable from the parent tree that the seed came from.

Now, Apple and pear trees are grafted for both cloning of the fruiting section as well as good rootstock. But most stone fruit grafting has cloning only as a secondary consideration - they are grafted mostly to be joined onto well-proven, high-quality rootstock that can produce lots of sap and confer resistance to certain diseases.

Source: am orchardist.

Yeah but the phrase refers to children who were raised by the parents, not the ones who got eaten by large birds and shat out in distant lands, which of course happens far more often than we'd like to think.

You're not wrong about seeds. The saying doesn't mention, refer to, imply anything about, or have anything to do with seeds, though.

Ummm, it says the Apple doesn't fall far from the tree, not the seeds don't fall far from the tree.

Yep, seems to me to hold up in the metaphorical sense as well.

Not arguing against the genetically inherited traits, even beyond the purely aesthetic/structural ones, like inclinations toward certain ways of processing information, nor do I ignore the fact that they're not 100% heritable. But even as such, nurture (which I view from the belief that the entire village shapes the person) can generate a completely divergent personality, and the breadth of development is directly proportional to the breadth of exposure samples (at least to my mind).

And let's not neglect the more practical similarities as well! Different types of flora require differently sized "privacy bubbles," areas of earth reserved exclusively for their individual sustenance, otherwise they'd essentially choke each other out. We can see something very similar in the development of children who are too closely bound to their family through mechanisms of excessive control, their potential ends up being smothered.

Edit: disclaimer, I'm working with 12th grade Biology and a Bachelor's in Theatre Acting as my sociology background, so I actually expect to have botched something up in what I said. Salt is advised.

The Apple doesn't fall far from the tree, but the seed rarely grows near the rind.

Apples are so fascinating! There is a fun section of this documentary on them: https://m.imdb.com/title/tt1421383/

Who thinks it's supposed to be a good saying? It's pretty much saying that person is a dick because they were raised by dicks.