That's one thing I took from your post that I agree with
Any idea that the algorithm itself has value in itself probably isn't the kind of thinking that's going to get you very far; the code itself is usually open source and available for free. Now, those who implement the algorithm early (miners that get in on the ground floor), that's where the value is. Not initially, because at that point, not enough people value the fact that someone solved a few computer puzzles. But if a bunch of "greater fools" coming along later and putting a value on the fact that these early miners have proven they've solved some puzzles, then that creates value "out of thin air".
It's about scarcity and about convincing enough people that there's value in this scarce thing. They used to pay people with salt (the source of the word "salary"), because it was scarce. As soon as something isn't scarce, it quits working as something that can store value and be used as a proxy for goods and services. The block chain is simply a means for "everyone" to verify that it's a legit member of a specific set of scarce things (bitcoin, in this thread).