The Rockefeller example, though frequently cited, is a red herring. Those companies were thereafter known as the "Seven Sisters" and not exactly known for truly competing with each other.

There was also a comment here I read recently about Rockefeller being a pretty activist shareholder, in the sense that he arranged meetings--using his considerable clout--among heads of the resulting companies, many of which were his most loyal former employees.

Right, ditto with AT&T. That's the point. Monopolies haven't always been able to resist being broken up -- but they have always been able to arrange the breakup so that the pieces don't compete and don't shift bargaining power to the consumer.

Minor nit. The Seven Sisters weren't all descended from Standard Oil of New Jersey although a number of them were.

Is that's the case then why don't companies voluntarily break up?

Companies break up all the time. Sometimes as a "spin off" where a part is let go on its own. Sometimes a division is sold to someone else who wants it. Companies are in a constant process of changing size based on what they guess is the best place to be next year.

Companies break up all the time, it's just that such moves are rarely sexy enough to break through into the mainstream news cycle. Take Hewlett Packard for example, the comapny's very existence is owed to its origin as a manufacturer of test equipment (calibration and measurement equipment) but they decided to spin off that core business unit in 1999 as Agilent (this move was the largest ever IPO in Silicon Valley at the time). Their decision wasn't made on entirely financial grounds either, the idea was actually that a smaller, more focused leadership team would allow the business to become more agile and thus more profitable than it could be while under the burden of HP's broad-focused bureaucracy.

To take that one step further, Agilent then spun off the electronic test equipment portion of the business (which was HP's original market when it was founded) as Keysight to focus on their life science divisions. Each of these decisions was made despite the spun-off division being successful under the greater corporate umbrella.

I'm guessing that the cited post-breakup benefits accrue from a renewed level of focus.

There are plenty examples of public companies breaking themselves up for this reason. e.g. IAC breaking off Match.com and ANGI Home Services. Service Master breaking off American Home Shield.

people form conglomerates too which typically underperform.

I guess it’s some combo of effort/risk? Collect a monopoly rent rather than take greater risk?

Your question is not unknown to economists and there is no clear answer.

Another possibility is an agency problem, where the company management is doing what's best for themselves rather than best for shareholders. (Just an idea, I don't know whether that's actually the case.)

This is a side effect that I'm willing to deal with. The problem with monopoly is not so much about the concentration of individual wealth in my mind, it's about the lack of competition between companies which make investment in R&D and innovation less of a factor to success.

Rockefeller rightfully became more wealthy when he owned a large portion of stock in very successful, but highly competitive companies, as opposed to an unchallenged behemoth. It would be like splitting your stake in Walmart into equal shares of Amazon, Target and Dollar Tree.

It's also interesting that when Rockefeller dominated the oil market and standardized it, the price of kerosene dropped dramatically. Rather than monopoly being negative for consumers, the competition had actually driven up prices and lowered quality standards as competitors sabotaged eachother

I think that was a function of the phase of the S curve.

Also remember his tying: he controlled all the tankers so even if you competed with him in petroleum products he controlled your (literal) path to market.