Joe is nothing if not a traditionalist. Alvarado is unproven and as you note, the only lefty, and Bradley is both more established as a set-up man and can pitch more than one inning. And I don't think Kintzler, the other "proven" closer, was ever really a candidate.
Hopefully Hector is set up for a good year (and age or injury don't get him) that gets him back to 2019 form. Light usage last season, new pitch. He hit his usual rough patch in 2020 but between the small sample and how terrible everyone else is he wasn't actually a disaster. The high walk rate and WHIP was probably from the one epic bad patch; career-low FIP and 0 home runs (two related stats). Strikeout rate still about the same as ever; was a lot higher in 2018 but that was his worst season.
Honestly it will be interesting to see if Girardi is flexible, other than when off days factor in, because it seems like he and many of the pitchers just prefer set roles. Closer/set-up/lefty, just like on the Charlie teams, with one more guy as the top 6th/7th option.