An invention exploding throughout the world upon the expiry of a patent is the primary feature of patents, not evidence that patents are bad. The whole point of patents is that after a brief monopoly period, the entire invention - detailed in the patent to a level sufficient to recreate it from scratch - becomes the public's to use.
Your example is evidence of patents successfully driving progress everywhere and working as intended.
I'd much rather things protected by trade secrets had been protected by patent instead. If that was the case, for example, I could buy coca-cola for the price of the store brand. But I can't, because the formulas are still secret and not held by the public, even after more than 100 years. The formula being secret serves only to benefit an entrenched multinational corporation and reduce competition - rewarding neither the public nor the original inventor.
Patents have a long history of abuse and very little evidence that they drive innovation. The case has to be made that their benefit outweighs their harm. My argument is that it doesn't.
As tofof said, that’s absolutely the entire point of the patent system. The original inventor (Watt?) patented his invention. For a period of time, he could use it exclusively. And then the patent expires and everyone gets to use it. Everyone wins.
The case for patents needs to be made empirically -- lets see where they actually drove innovation. In general you will see massive innovation as soon as a patent expires.