Look at it this way...
(1) Basically any class on offer at your gym, taken daily, will get you fit, sexy & healthy. Pilates, weights, swimming, wall climbing. They all work good, as long as you keep doing them and don't quit.
(2) Quitting is extremely likely. Most of us quit most of the exercise regimes we start.
Given these two points, the only thing worth optimising is "how not to quit." A good start is aiming for that "sweet spot" where you feel satisfaction, but not soreness or burnout. If you have to make yourself take a recovery day, that's a good place to be. Obviously also life stuff. Scheduling, social stuff, etc.
For most people most of the time, running out of discipline and quitting is the failure point. The relative merits of running vs weights vs judo are trivial relative to the merits of continuous exercise habit throughout your life. You'll naturally gravitate towards little optimisations and improvements anyway, if you keep showing up.
If you're a pro athlete, where showing up is a given, then the difference between high rep and low rep matters. Otherwise, it's like premature optimisation.
Even for pros, like professional writers, the most common advice relates to showing up every day.
You do the cardio to build more endurance, a stronger heart, and apparently a more efficient use of the oxygen in your blood.
TFA didn't seem to be about weight loss; it was about declining health. And in that case, virtually any consistent exercise would be an improvement. Whatever it is that gets someone off their sofa regularly is a good starting point. If that activity is weight lifting, then perhaps they will enjoy the extra benefits of better strength, higher metabolism, a feeling of more energy, etc.
So it's better to do something suboptimal that you enjoy, than not do the optimal thing because you hate it.
And cardio definitely helps with weight loss, because all the bodybuilders do it for cutting.
For me it's bodyweight excercises and running. And I don't really care if there would be something else that's better.
And about the cake example, you probably want to replace that with healthy food that you enjoy, not with the most healthy that you detest. Otherwise you will drop out immediately.
2) The 2nd part about enjoyment vs dropping I just completely disagree with.
2.1) Enjoyment often builds up with confidence and success, especially in the areas where you make rapid progress as a beginner, like weight-lifting or cardio or most PT really.
2.2) In general, this mindset where you only do things as you enjoy and don't try to develop any grit is terrible, especially for people who don't start out with an advantage in a given area (health, financial, smarts, mood, etc). And more so for people who have self-inflicted problems in a given area - the problems that stem from doing what they "enjoy".
For an example, my understanding is that weight lifting is better for weight loss than cardio, contrary to the popular perception... if your goal is to lose weight, you'd better do what works best and not what you enjoy, or at least choose the activity that you enjoy most out of the ones best for the job.