Daffodils have lost the need to be pollinated because they are grown from bulbs! The only reason they still have flowers is that the bulbs are selected from those that produce the nicest blooms. Plant breeders keep seed-fertile varieties in order to continue hybridizing. But these don’t make it to market: only bulbs grown out from them will be sold.
You don’t see a lot of bees or other pollinators on hybrid roses, either. They are propagated almost entirely from cuttings. Incidentally, if your hybrid rose gets frost-killed, but the rootstock survives, you’ll have a nice multiflora with tiny white blossoms, heady scent and a cloud of bees around it.
It is incorrect to say that daffodils have lost the need to be pollinated because they are grown from bulbs. No cause and effect relationship exists between the two. Many, many plants can reproduce by either vegetative or sexual means, but plants that are reproduced by bulbs, corms, rhizomes, or leaf cuttings do not lose their ability to reproduce by seed because of it. In fact, except for occasional mutations, each vegetative reproduction is a clone of its progenitor with the same seed-producing ability.
What daffodils (and many other flowers) have lost in the process of selection and hybridization is the ability to attract insects with sweet-tasting nectar. The loss came about when breeders selecting for specific flower traits ignored the nectar-producing capabilities. But most daffodils still produce viable pollen and seed.
Plant breeders are not keeping the fertile varieties all to themselves. They have cultivars which are particularly useful, but they are not sacrosanct. When I was breeding daffodils I started with just the blooms in my garden. It is easy to get seed: just take a toothpick and transfer the pollen from one flower to the stigma of a different flower. It is the same thing the pollinators would do if they were still attracted to the blooms.
You can tell when you get seed because the ovary gets really large; a seed-bearing daffodil is easy to spot and the seeds are big and easy to handle. You can replant the seed right away or store it and plant it in the fall. In the spring you will get a new daffodil plant that looks a lot like a blade of grass. And in seven or eight years it will bloom for the first time—which is the real reason you can’t find daffodil seeds at your local garden store: who would buy them?
Sometimes daffodils will cross after a visit by a curious insect. If you have a lot of daffodils, check for a very fat ovary after the flowers have withered and dried. Collect the pods before the the seeds drop to the ground.
Now about roses. You say if your rootstock survives “you’ll have a nice multiflora with tiny white blossoms, heady scent and a cloud of bees around it.” That may be true, but it depends on the rootstock that was used. Different rootstocks are favored for certain climates and soil types.
Nevertheless, if your rootstock had pink flowers before it was grafted, it will have pink flowers if allowed to re-sprout. If the rootstock was a variety not particularly attractive to insects, it won’t suddenly become attractive if allowed to re-sprout. The important point is that you don’t know what kind of flower you will get from your rootstock unless you know what species or cultivar it is.