There has to be someone who is breeding a decent line of Rocks who are not right from the hatchery, someone who doesn't necessarily have the old heritage lines (which I adore, of course), but who have good quality homestead Rocks who have a good laying history. If my own were still with a BR rooster and laying enough, I would have no problem offering eggs from them. Mine are not Leghornish in type at all. In fact, Amanda that I mentioned is a tank of a hen. Of course, you won't see the super precise "test pattern" barring on them, though Amanda's is finer than most, but the generations one or two from the hatchery are better birds as far as health.
You cannot beat an egg a day. My BR hens in their prime (first three years) lay an egg a day, like like a good production Rhode Island Red. I've had them running side by side and they lay as many eggs as the RIRs. I haven't had a LH, however, as I said, even a RSL doesn't lay more than one egg per day, 7 days a week. Fern, who is 4 years old, until this year, gave any LH on the planet a run for her money.
So, though it does vary, and as Fred said, the Rock is a dual purpose bird, not technically just a laying breed, an egg a day is all they lay, no matter what breed you get. I do wish I was in a position to breed from these BR hens I have who are stellar layers because I think you'd be thrilled with the results.
What I'd love to do, really, is cross those hatchery descended hens with my Indy, who has the Stukel lineage on his mother's side, and the stupendous laying ability of the Delaware on his sire's side, and see what happens with those daughters. The Delawares lay earlier than the Rocks I've had (17-22 weeks they all start, it seems, in this line), but this is the Rock thread. Unfortunately, I may not be able to do any of the breeding projects I have in mind due to monetary constraints. Can't afford the feed.