> Trade secrets were invented as a riskier way to extend your monopoly by giving up government protection.
You're definitely mistaken on that point. Trade secrets enjoy protection in the law, both in the US and worldwide:
https://www.uspto.gov/ip-policy/trade-secret-policy
> If the government is going to give trade secrets the same protection as patents (or even more, because patent infringement doesn't come with jail time), companies have zero motivation to publish.
Despite both forms of IP enjoying legal protections, there are many reasons to prefer trade secrets over patents or vice versa.
It's much much easier to accidentally lose trade secret protection by inadvertantly divulging those secrets, so in that sense patents are more "durable".
You also can't use trade secret protections to prevent reverse engineering, so any invention that's easily observable and reversible is not suitable for trade secret protection.
Trade secrets also can't be used to protect from independent invention, so if someone else discovers your trick, you have no recourse.
Conversely, trade secrets apply to things that cannot traditionally be patented. The classic example is, of course, the recipe for coke, as recipes in general are not patentable subject matter
Trade secrets also have no expiration date, hence again, Coke.
Obviously this is a deep well and I've only just barely scratched the surface.