Definitely, but I know some world class golfers, like Pretend I’m A Caveman Easy Lazy Halloween Costume Party shirt who won the US amateur, then went on do alright in tour (never won like the original post guy but made cuts and had top 25 finishes in some majors) and he was a head pro, teaches golf to this day (top 25 golf school in US for 10+ years), but it is definitely not his primary source of income (has a new business that he spends much more time on). So while this strengthens your first point of finding other gigs after leaving the game, it goes to show just how elite you have to be to making anything near 100k working so few hours as you suggested.
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As far as your first point, I totally agree they are not doomed or anything but I would argue way more people assume pro athletes ‘never will have Pretend I’m A Caveman Easy Lazy Halloween Costume Party shirt ’ then assume ‘they can never work again’. All I’m saying is to a lot of people it sounds like these guys have it made when they see their salaries; retire early, live lavish,etc. Don’t think people see the million dollar a year salary and imagine them working at a grocery store or looong mundane hours in a pro shop handing out tee times and tallboys. So there are more factors at play here and having to work after their sports career is certainly commonplace. They usually do not have the skill or experience for high paying jobs in other sectors, but this is balanced by golf jobs that pay alright like you suggested.