"At the heart of any patent, there should be some trade secret."
I think most people would disagree with you. The majority of ills in our patent system today are due to patented "trade secrets" [...] the workings of most useful INVENTIONS usually become pretty obvious at the point the invention hits the market; thus the need for a patent in the first place.
If the working of the invention become obvious at the point the invention hits the market, society has no reason to offer the inventor patent protection in exchange for being let in on the secret. Only in cases where the trick wouldn't be obvious to a practitioner skilled in the applicable arts do we have any reason to say "Oh, come on, just tell us how it works and we promise not to compete with you!" -- in other words, grant a patent in exchange for full disclosure.
Patents are supposed to be what we grant the inventor in exchange for their revealing a "trade secret" that we wouldn't have otherwise been able to figure out.