The usual poster child for patents is drug development. It costs about $1 billion to get regulatory approval for a drug (this is also why drug costs tend to be high). Once you know the formula of a drug, it's not particularly hard to work out how to make it, and the marginal costs of actual production are almost nil.
The main value proposition of patents is that you entice inventors to make their inventions public for promoting further innovation, with the cost to society of given them exclusive practice for a short time. The problem with trade secrets is that reverse engineering exists, is generally legal, and is surprisingly easy. Give me a shipping binary and it's effectively equivalent to giving me source code.
I recently was thinking about patents, and software patents in particular. It's clear that the current patent system doesn't work very well here. SCOTUS has heard several cases about this general area of patents, and has found all of them distasteful (note that State St. was not a SCOTUS decision, and in Bilski, SCOTUS went out of its way to complain about how bad State St. was), while still struggling to be able to articulate a useful test.
The problem with software patents, in a nutshell, boils down to the fact that an invention like, say, the Enigma machine is the sort of prototypical invention that everyone would agree is patentable, while it's not clear that the software analogue should enjoy the same patentability (leaving aside questions of novelty, here). Should we prejudice a modern inventor just because he implements his useful machines in a virtual question, they ask, with the implicit response hopefully being no. And it's that response that drives SCOTUS to shying away from categorically saying that this sort of stuff that's never patentable.
And the answer I would give is yes. It is inherently more difficult to realize an idea in a physical domain than it is in a virtual domain--after all, I can try many different implementations in an afternoon (it's called recompiling). Furthermore, one of the great revelations of the information age was that you can equate many different concepts with relatively simple encoding systems--think about how we can use integers to represent, say, floating point numbers or strings. The essence of patentability is that you had to figure out something new, which is to say you had to realize an abstract idea into something concrete in a new way.
The downside is that this suggests that software should be patentable, although the bar should also be recognized as being much higher. And when you go back and you read the Alice decision, you can see SCOTUS sort of reaching towards that idea: you have to do something inventive with the abstract idea to meet §101 requirements.