yes you might be looking at it backwards, it probably is a wash if you live to the average age (if everyone in your family tends to be long lived though you may want to wait). See reason #2:
https://www.fool.com/retirement/2018...ty-benefi.aspx
Now I would suspect A LOT of people might wish to work until 65 because they want to collect that employer provided medical insurance until they can finally get Medicare, but the affordability of healthcare options is a separate issue.