While a company that controls the majority of a market may be the text book definition of a monopoly, it's the the legal definition in the US. The US law recognizes that a company may naturally (and legally) gain a majority market share (even 100%) and be left alone. It's only when a company with such control over a market uses that to leverage control over another market that it becomes illegal under US law.

Standard Oil owned 90%+ of the oil refineries in the US (they never did drill for oil) yet that wasn't why Standard Oil was broken up. They were broken up because they were using their influence with oil to control the train industry, specifically, train transport of oil. [1]

Microsoft wasn't threatened with breakup over their operating system monopoly on desktop computers, but because they were using that influence with at attempt to control the web browser industry.

[1] And ironically, it was the breakup of Standard Oil that made John. D. Rockefeller the richest man in the world. He was also responsible for saving the world's population of whales. [2]

[2] Half-serious here. Whale oil was big business, until Rockefeller made petroleum products cheap enough to supplant whale oil as a product.

During the rise of standard oil the price of oil went down, it did not go up. Competitors fought and complained that they couldn't compete because standard was vertically integrated and got it broken up.

But the price did not go up.