> It is the case that if you do a flow-insensitive analysis of variables over SSA, it will be equivalent to a flow-sensitive analysis of variables, because of the static single assignment property.

you're saying the same thing i'm saying - the question/issue arises from value numbering and naming. see "engineering a compiler" page ~400 where they discuss the benefits of SSA for value numbering: https://imgur.com/a/bPabq7D

> I don't think dense vs sparse analysis is the same thing as the use of the word "sparse" in the post.

it is - the allusion/claim in the post is that SSA is sparse because you don't need to keep track of facts/metadata for all variables at all program points. that's because of the same thing: SSA uniquely locates/identifies values and therefore you can uniquely map between SSA ids and metadata. so you don't need to have a table of stuff that's updated at every program point (like you do in dense analysis), just along control-flow/operand/result edges.