There are utility breeds, but they could never be farmed on an industrial, supermarket supplying scale.
They tend to eat more than egg-type hybrids, and produce smaller eggs in far fewer numbers (eg. Up to 200 a year as opposed to 300+ large eggs).
They also take a lot longer to rear to a suitable weight, months as opposed to 7-10 weeks like specific meat hybrids.
Margins are so narrow in farming that farmers are forced to cut back so often that we have ended up in this situation of animals being massively exploited and labels and boxes are an exercise in finding wordy loopholes (eg outdoor bred pork - piglets are conceived outdoors, but born and reared intensively indoors, consumer thinks they are buying higher welfare meat).
IMO, if you're buying from a supermarket, buy organic, burford Browns, those brands. I don't think there is much difference buying caged or free range tbh, it's only a marketing spin with improvements for only a few chickens.
If you can find local chicken keepers, the eggs will be better quality and probably cheaper (we sell ours for £2 a dozen), but as most people have hybrids (we have a few) they will still have come from hatcheries which need to dispatch all the male chicks. Unfortunately there is no viable alternative to killing male chicks, as they are, in farming terms, useless, unless they are meat hybrids, and even there females are seen as superior as they have lower bone:meat ratios.
If there was ever an enthusiastic land owner who could set up a system using utility birds, I imagine there would be a market in specialist shops, but the margins would never work for this to,become a mainstream option.