Can you provide a few examples of the ample historical evidence for that "inevitable result"? I'm looking for one or two cases where a private monopolist entered a competitive market, managed to shut down competitors with predatory pricing, and then raised prices afterwards to higher levels than when they entered the market.

This is one of those claims that sounds plausible, but I've yet to encounter a historical case of it actually occurring.

That's because it hasn't happened. It is simply a highly-plausible fantasy used to justify government interventions in fully-functioning markets. Economist Thomas DiLorenzo has actually studied this, and has found that, in the vast majority of cases, monopolies are associated with a dramatic (edit: permanent) reduction in prices. He found only two cases that actually followed the "predatory pricing" script (edit: that is, where prices dropped over time and then rose when monopoly power was achieved) — and those were trivial monopolies in the markets for matches and castor oil in the early 20th century.

(Edit: remove FTC comment, as it is besides the point and not strictly accurate)

Microsoft and Internet Explorer is pretty close. Browsers sold for money. Microsoft entered the browser market and undercut it. Through market dominance they owned the market requiring anyone that wanted to access some parts of he web intact on Windows.

As a consumer now, is the problem that I have to save up my money and carefully choose which expensive web browser to "buy"?

At most, that's evidence of a new dynamic coming to a market, but I don't see the evidence of consumer harm from the phase 2 raising of prices in the browser market.

Ok, internet explorer.

At what point in history did microsoft drive out all its competitors, and then raise prices?

Oh wait. Never. They never raised prices and kept internet explorer free forever.