That's the thing I can't get past with most of your arguments on here. If an algorithm is truly unique and worth the patent then in reality it shouldn't need the patent at all.
I also don't understand the "I invented an extremely complicated algorithm for solving X" mentality. We all stand on the shoulders of those who came before us in solving more and more complicated problems. Without the software, algorithms, and general knowledge of computing that have been made available to us we'd not be able to take that and build ever more complicated systems on top of that.
Besides the probability of independent invention, the other key difference between the two cases is that in the former, you could never sell someone the idea of e-mail notifications in the absence of patent protection. In the latter case, the idea itself is very valuable--the patent just provides a legal structure that facilitates transactions.
As for the "standing on shoulders" angle, I think it's all about the difference between applied research and fundamental research. There isn't any money in giving away the fruits of your labor for the good of humanity (which is why top students from Harvard, MIT, etc, head to investment banks rather than fundamental research labs). And even amongst the altruisticly-minded, some fields are much more engendering of generous feelings than others. Nobody thinks the joy of blessing the world with more efficient filters for chemical plants is sufficient compensation in and of itself for the work put into designing those filters.