This is both interesting and (I think) an important thing to know about science: plans and strategies are systematic, but discoveries sometimes are and sometimes aren’t. In particle physics, the Omega baryon and Higgs boson were discovered in deliberate hunts, but the muon and J/psi were serendipitous. The ratio might be about half-and-half (depending on how you count particles).
Thinking about this, I have two half-answers, which may be leads as to why sweetener discovery might be discovered by serendipity, even though there are systematic searches for new drugs.
Discovery depends, to a great degree, on your detector, and I don’t think there’s a better detector of sweetness than the ones in our mouths. Presumably, searches through virtual (not synthesized) molecules can be faster, and if the identification algorithm can accurately predict activation of the sweetness receptor, then it could outperform detection by taste only because it’s faster than synthesis. But virtual drug discovery is still an open problem, still under development...
Maybe there are, in nature, only a few sweet molecules, and they were discovered early. Going through the list of artificial sweeteners you mentioned, below are the discovery dates. When were most of the systematic drug searches? Did it cover this timespan, which seems to be in the early and mid-20th century?
Saccharin: 1897
Cyclamate: 1937
Aspartame: 1965
Acesulfame potassium: 1967
Sucralose: 1976
(This suggestion also has an analogy with particle physics: hundreds of particles were discovered in the 1950′s because accelerators had just been invented that could illuminate the strong-force mass range, which has rich phenomenology. At the current frontier, though, there are very few particles.)
Other comments in the comments section that sound quite likely to me are: (1) perhaps the very sweet compounds could be smelled, which prompted chemists to try tasting them (@mako-yass), and (2) maybe some of these origin stories are scientific folklore (@d0themath). Scientists, who are very concerned to get the description of physical reality right, are surprisingly cavalier about describing their own history in an accurate way.
I’m surprised that Scott Alexander’s blog post didn’t go for what I think is a more obvious connection between conservatism and conservationism: religious fundamentalism.