For someone my age, who grew up as the last of the old guard of vertically-integrated conglomerates, and also the odd "diversified" conglomerates were breaking up, it's really a wonder to imagine the scale of a business like (the original) AT&T.
And to be clear, I know we have our share of giant companies today, but there's something so much more honest about a 1960 AT&T, compared to say, Apple, Microsoft, or Google, who while maintaining massive market share, don't even employ the people who sweep their floors or serve meals in their company cafeterias, let alone those who manufacture any of their hardware. So, the large corporate footprints today feel kind of like thin envelopes which serve to capture as much of the profits as possible from a large set of related businesses, without having to get too involved with any of the details. There's nothing I can point to specifically that's wrong with this apparently efficient arrangement, but I just think I like the old model better.
IMHO, the important thing that's missed without vertical integration is shared motivation and easy communication between design, manufacturing, operations, repair, and research.
When the repair team can talk to design and manufacturing, common repairs inform changes so that repairs are less frequently needed and/or easier and cheaper to perform.
Having such a broad scope of business enables a research arm that can do more basic research, because anything interesting likely has an application somewhere. Additionally, a broad scope of business means lots of opportunities for directed research on new or tricky problems that come up.
Having employees run cafeteria and janitorial and etc is valuable for someone like AT&T because they can study how those sorts of businesses use the types of communication products AT&T provides. As an entrant into the computer services market, having access to captive customers for say restaurant inventory management and what not seems helpful, etc.
Vertically integrated dominant firms come with problems, too, of course.