If you're doing cardio for VO2 max or endurance training, end-of-set effort generally counts for more (though a proper warm-up sets you up for success).
For skill activities, cumulative experience matters, but form breakdown with fatigue limits single-session gains. Going flat-out all the time isn't beneficial.
For weight training, hypertrophy (size/mass increase) seems to be based on time-under-tension and total volume (so that last set matters), while strength and power training rely on motor-unit recruitment and/or speed, both of which are maximized when you're relatively fresh.
Even for hypertrophy and endurance, there are diminishing returns to additional sets. Somewhere between 3-5 sets for a given exercise and you're not going to see much additional advantage. A training session may include other movements to stimulate muscle from different angles, at different ranges of motion, or independently of other synergist/agonist muscles.
The article is discussing one aspect of one form of exercise. The conclusions it reaches (happiness / mood influences of cardio) aren't generalizeable to either all effects or all forms of exercise.
The last 20 minutes matter if your goal is performance, or muscular hypertrophy. Then yeah, those last few reps, done through clenched teeth and sweat dripping in your eyes, are the ones that matter.
If it's for health and well-being, it's the fact that you're doing anything at all - hence "the first 20 minutes" rule.
The last twenty minutes improves your endurance, strength, and/or power (depending on the activity), but the first twenty minutes provides the general health benefits.
> Makes sense
Does it? I'd say the last twenty minutes of exercise is what counts - it's the difficult part.