Brian took a second postdoc at UCLA: https://www.math.ucla.edu/~brianrl/
That would be his 3rd postdoc, after Columbia and Chicago. Is the struggle worth it?
He clearly thinks it is. I know any number of people who decided to leave academic math after postdocs at Chicago-level places, and they're all making a killing at hedge funds or in Silicon Valley. Heck, the second-tier PhD students at my MLM school have no trouble finding those kinds of jobs (though most of them do Silicon Valley stuff -- I think the major hedge funds prefer elite postdocs/PhD's). Brian isn't an id*t, so he knows that option is always open to him.
Looking at BL's publications, outside the two papers coauthored with senior/big stars there is a steep drop off of significance and quality. I guess a top-20 math department might be reluctant to hire him due to this lack of "insurance" on his productivity.
While there are rare cases in which a single big paper significantly elevates one's career, the paper has to be single-authored and with top-level significance. (Examples are Yitang Zhang on prime gap, and Viazovska on sphere packing.) Outside those cases, hiring and tenure at top-20 places require sustained productivity at a high level. In that regard, BL is not very competitive. Since he is now a postdoc at UCLA, one can look at who UCLA recently hired as new APs. See Pavel Galashin or Hong Wang. Both got their PhD after BL. Those are the qualifications for a new AP at UCLA, which is not even in top-10.
A 4-time Putnam Fellow went into utter obscurity in mathematics while the people who weren't as great at competitive math went on to become professors. How weird.
