Yes, I think C25K and the "just run" sentiment in general is missing half a dozen asterisks about this aspect. Like "except don't run on concrete for the first year", or "except do this progression of exercises for feet and tendons for 3 months before you start doing continuous 2-3k", or just "hire a trainer to get you started".
I've never been overweight, been active as a kid, was in increasingly good physical shape throughout my 3 attempts to start running over the years and got injured for months every time. By the last attempt I was taking multi-hour walks as a habit, lifting weights 5 days a week, watching my sleep and diet. And heart rate monitor has shown that I straight up didn't have this magical "easy run" heart rate zone available - brisk walk was well below 120 bpm and even jogging in place got me over 130.
C25K is great for what it is, but I feel what it is is not enough to start running safely.