My impression after reading James Kaplan's Sinatra biographies is that the sub-par lyrics wouldn't be something that would have grabbed Sinatra.
By 1977 Frank wasn't recording as much and Brian wasn't hip or commercially successful then.
In 1966/1967 Sinatra probably would have been have somewhat interested in Brian writing a song for him if that would have meant a hit record.
But both of them wanted hit records, maybe Sinatra a little more at that point. That's one explanation for why Frank and/or his management allowed the disco singles to see the light of day, and why minus a masterful fluke like "New York New York" a few years later, Frank went back to Quincy Jones to get a more "contemporary" sound in the early 80's. He definitely wasn't doing it for his fanbase, who were and perhaps always will be perfectly content with hearing Frank as he was heard on Capitol backed by Riddle and May arrangements, live or on record. I'd also add the "Duets" project to the examples of Frank wanting a hit, on those he cast a wide net to grab multiple genres and successful performers he could put on an album.
I seriously think Frank as an interpreter of songs and lyrics was always on the lookout for new material that he thought would work for him, even further songs which he thought could be a hit. In that way, who knew whether or not something written by Brian Wilson would catch his ear any more than something by George Harrison, David Gates, Paul Simon, Jim Croce, John Denver, or anyone else from the 60's pop/rock field whose songs he covered? It didn't hurt to try, short of actually presenting the song to Frank.
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