The reason most apples are produced from grafted trees is that apples don't breed true.
In a large number of crops, you have "lines" of crops. Basically, if you breed two plants of the same cultivar together, their offspring are similar enough to both parents that it performs like the parents. The reason for this is that these crop lines have been interbreed with each other for long enough that the population is self consistent, and the important alleles are present in frequencies that mean all progeny are likely to inherit them.
However, the types of apples which are sold commercially are not from these sorts of cultivar lines. Instead, they've been obtained from "sports". That is, the chance production of either a particular hybrid gene set, or sometimes from random mutations that happened on an adult tree of another apple variety. For example, the Granny Smith occurred from a chance seedling which was discovered by Maria Ann Smith.
These apples don't necessarily have "consistent" alleles. For example, it may be heterozygous for certain genes. If you have Aa alleles at one gene, if you self-pollinate the plant, you're going to get a mix of AA, Aa and aa genes in the offspring, the last of these isn't going to be the same phenotype as the parent. Now recognize that this is happening at multiple genes across the entire genome, so there are many chances to get non-parent-like allele combinations. Add to this the issue of co-dominance, where the heterozygote has a different phenotype than either homozygote (that is, BB isn't like Bb), and the chances that an offspring has a gene with a non-parent like allele combination is pretty high.
There's a further complication that some apple varieties like Honeycrisp are self-sterile. Even if Honeycrisp could theoretically breed true, there's no way for it to fertilize itself, meaning that all fertilization events are hybridizations.
Now you can certainly grow apple trees from seed. The planted seed will grow up into an apple tree, but the chances are that the combination of alleles it received by random chance from its parents will not result in an genotype that produces any commecial apple phenotype. Instead, you're likely to get regression to the mean, meaning the apple tree will be like the ancestor of apples - a crab apple, or at least crab apple-like. - But there's a small chance that it will have commercial apple-like properties, which may or may not be like the parent. This is how new apple varieties are formed, after all.
The only way to guarantee that the genotype of an apple tree is close to the parent plant is to propagate it by cloning, and the easiest and cheapest way to clone trees (at least apple trees) is by grafting.
(As a final note, remember that the seeds get their genome from the flowers and the cells which produced the flowers. The genotype of the rootstock - grafted or not grafted - has no bearing on what genes are present in the seeds. You'd have the same issue with apples breeding true even if the parent tree was on its own rootstock.)