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The answer, at least a partial one: eggs. Eggs, specifically egg yolks, play several roles in homemade ice cream. You can make tasty ice cream without them, but there's a reason that almost every recipe published in the last 50 years calls for them. After water, egg yolks are mostly fat and protein.
This also means that egg yolks prolong the shelf life of ice cream in a freezer, since they inhibit the thaw-re-freeze cycle that ruins ice cream's creamy texture. So eggs have a lot going on. And on top of all that, they taste good, adding a rich, custardy note that is often desirable in flavors like vanilla.