By "Bro Splits", it seems that you are referring to a split routine wherein a different muscle group is targeted each day with machines or dumbbells, completely avoiding any compound lifts.
Do Bro Splits work? Well, that depends on what you mean by "work", which of course depends on your goals. If your goal is to get sweaty and burn a few calories each day in the gym while avoiding boredom, then Bro Splits definitely work. If your goal is to put on a little bit of muscle mass over the course of months of training, Bro Splits might work (depending on the details of the training schedule). If your goal is to gain some hypertrophy in specific muscle groups strictly for aesthetics and not for useful strength, then Bro Splits might work (again depending on the details of the training program).
If your goal is to build useful strength as fast as possible without wasting time, then Bro Splits do not work. This is especially true of routines where a given muscle group is only targeted once per week.
The problem with isolation exercises is that we do not activate our muscles in isolation when performing normal movement patterns. When moving our bodies and exerting force against external resistances, we activate multiple muscle groups at the same time. To stand up, we activate our quads, our hamstrings, our hips, our calves, and our back. To pull something off a shelf, we activate our biceps, our triceps, our shoulders, our abs, our back, our quads, our hamstrings, etc. Normal human movement patterns always involve multiple muscle groups working in concert. When trying to maximize useful strength, all muscles involved in the movement pattern need to be strengthened. Otherwise, the weakest link will limit useful strength. The problem in trying to accomplish this strictly with isolation exercises is that it's basically impossible to know how much to strengthen each muscle group relative to the others.
Let's say your goal is to be able to lift 100 lbs from your chest over your head. How strong do your various muscle groups need to be in isolation in order to achieve that goal? How much weight should you be using with tricep extensions in order to achieve that goal? How much weight should you be pulling on the deltoid machine in order to achieve that goal? How much should you be pulling on the pec fly machine in order to achieve that goal? It's essentially impossible to answer these questions.
How strong should your triceps be relative to your biceps in order for the two muscle groups to be in balance? How strong should your quads be relative to your hamstrings in order for the two muscle groups to be in balance?
Attempting to build useful strength strictly with isolation exercises is essentially impossible, because it's impossible to know how strong each muscle group needs to be relative to its complementary or supporting muscle groups, and it is often difficult to mimic useful movement patterns using isolation exercises.
The most effective way to build useful strength is with compound movements. There's no guesswork needed to determine how to balance complementary or supporting muscle groups. All muscles involved get trained at the same time and to the degree necessary to complete the movement in question. The movement patterns are also natural. People squat. People pick things up off the floor. People lift things over their head. People push things. The compound lifts that mimic these movements are the most effective way to increase useful strength.
As for why the "lean, athletic" types prefer Bro Splits?
Well, I'd argue that looking athletic and being athletic are not the same thing. What you're probably observing is people with low bodyfat who are trying to enhance the aesthetics of specific muscle groups. But they are probably not very strong, and if they're athletic, it's despite their Bro Split training regimen, not because of it. But Bro Splits certainly could work for them, if their goal is to gain some hypertrophy in specific muscle groups.
The most effective way to increase general strength, for anyone of any age, is with compound barbell lifts (squat, deadlift, press, bench).
Are split routines in general bad? No, they have their place. Split routines are a perfectly legitimate (and effective) way to train around scheduling difficulties. Training three times per week is ideal, because it maximizes rest between lifting days. The downside of this is that each lifting session will get to be quite long, especially as the rest times between sets increase. A split routine typically separates upper-body-targeted lifts from whole-body lifts, and has the trainee lifting more days per week. The upside is that this shortens each session to a more manageable length. The downside is that rest between sessions is less than ideal. When you do bench and press one day and squats and deadlifts the next, your back didn't really get complete rest on the first day like it would if you were taking a complete day of rest prior to a lifting day.