It seems like a great idea — why buy a $35 apple tree, for example, when you can just buy one for a couple of bucks at the store and plant the seeds. But unfortunately, it’s not nearly that simple in reality.
Most fruit trees are hybrid varieties, and do not reproduce reliably from seed. It’s similar to people — you’re not an exact replica of either of your parents.
In a lot of cases, you actually lose the best traits of the parent — vigorous growth, good quality fruit, or disease resistance.
Another reason that growing apples, peaches, cherries, etc. from seeds of produce from the grocery store is that it takes a long time for them to first bear fruit. So you may end up waiting years for your tree to give you harvests, only to find it’s mediocre fruit.
Additionally, many fruit trees are grafted onto a dwarfing rootstock. That means the tree is actually growing on another variety’s root system; this root variety keeps the tree smaller (only 15 to 20 feet tall, for example, instead of 30 feet or more).
That said, if you have the patience and space for from-seed fruit trees, you can certainly plant the seeds and see what you get.
Note: Some gardeners do this with tropical fruits for low-cost houseplants. Avocado, mango, papaya, and starfruit, for example, all grow readily from seed and make attractive houseplants!