The real tap root is based on the genetics of the tree. Most trees don't have a central root that goes straight down. Those kinds of trees are very hard to transplant. Pawpaw, madrone, and walnut are examples. If you successfully transplant them, and I have, they still have a central tap root that goes straight down. An apple tree will never have a central tap root that goes straight down. It will have many roots. Some will go deeper than others. It doesn't depend on whether it is grown from seed. I have dug up many apple trees, both from seed and that had been transplanted. They are just different species of trees that will do that.
While it is true that the potential for the development of a central, deep growing tap root is genetically influenced, several environmental factors also influence the development. Not all tap roots are created equal, and, it is safe to say that not all species that are generically predisposed to develop a tap root will actually develop a deep tap root. For example, a well-developed hardpan below the surface can stop the downward growth of a tap root. In this case, lateral branches off the tap root will form the bulk of the root system. Other factors may similarly affect the development of a tap root. Or you can sever the tap root. Once the tap root is severed, it is, in fact, lateral root branches that "replace" it. These roots of lateral origin may grow downward and function in lieu of the tap root, but they are not the original tap root. Roots are, after all, typically negatively geotropic and are generically programmed to grow downward. So, in this case, components of the lateral secondary root system take over some of the function of the original tap root.
Similarly, roots from cuttings will NEVER form a true tap root. Instead, these adventitious roots form an extensive adventitious root system that grows both outward AND downward, but you cannot really call these downward growing adventitious roots tap roots. A true tap root comes only from the embryonic root.
Personally, I've had no trouble transplanting plants with or without a tap root, with a severed tap root, or cuttings with no tap root. The sensitivity to disturbance of the root system is also genetically determined, but it does not really seem to be linked to whether or not the plant has a well-developed tap root. Starting onions from dug up, disturbed small plants that have no tap root is common. Whereas other plants such as poppies and paw paws are known to be sensitive to root disturbance. Apples are known to be easy. Just as the genetics of a plant determine what method of vegetative propagation you use.
Correction from my previous post: "negative geotropism" should read "positive gravitropism" since roots generally, not always, respond with growth in the direction of gravitational pull. "Geotropism" implies a response to a geological factor.
I'm having a go at some direct apple seed planting this year using seed from local varieties (in my borrowed garden). I'm pretty sure that if I planted them unprotected they'd get eaten by mices straight away, so I've given them half a chance by planting them inside a 'bottle cloche' - a cut off pop bottle that has already served as vole guard for some of my trees that have now outgrown them. With top and bottom removed I get a wide tube that when Just pushed into the ground makes a safe area for seedlings.
Assuming I get some to germinate and grow, I expect it will be ten years here before I actually get to try the fruit, but coming off local stock the new trees are a little more likely to be tolerant of local conditions....any trees at worst will be rootstock for grafting better fruit onto.