You're forgetting about the stick, namely, the literally armies backing these massive shipping companies.
If you're going to run an extortion racket, you need the power to secure yourself against the inevitable challenges to your station. Egypt is in no position to handle and armed threat from the US, China, or even most European nations. Their government would be toppled and a sympathetic one would be installed who would lower shipping prices to something on the cheap side of fair.
The Suez Crisis's failure by the British and French had nothing to do with Egypt beating them militarily, and had everything to do with American pressure. One of the West's biggest strategic failures.
The Israel, British, and French insurrection completely dominated the Egyptians. The US wanted to carry favors with Egypt to prevent them to falling into the communist sphere, so it applied a pressure campaign against the British and French that completely wrecked the European economies (and from which they never really recovered). It didn't work, Egypt did not become an American ally in any meaningful way, and instead the West lost control over one of the most important shipping lanes in the world, turning it into a corrupt mess where you have to pay for passage in cigarette boxes and bribes.
It was one of the biggest foreign policy fuck-ups of the USA, in my opinion.
If you're going to run an extortion racket, you need the power to secure yourself against the inevitable challenges to your station. Egypt is in no position to handle and armed threat from the US, China, or even most European nations. Their government would be toppled and a sympathetic one would be installed who would lower shipping prices to something on the cheap side of fair.