I am pretty sure that extra properties like trapdoor mentioned in the footnote are actually more important here than just the average complexity part. There is some work on building something with high average complexity out of something with a small known area of high complexity instances; I don’t think there is any widely-considered-plausible plan for inserting trapdoors (what we want for public-key encryption) into arbitrary NP-complete problems.
I am pretty sure that extra properties like trapdoor mentioned in the footnote are actually more important here than just the average complexity part. There is some work on building something with high average complexity out of something with a small known area of high complexity instances; I don’t think there is any widely-considered-plausible plan for inserting trapdoors (what we want for public-key encryption) into arbitrary NP-complete problems.