the sea of wannabes

You don't need a university degree to do personal training well. You do need one to help high-risk people, those recovering from strokes and so on. But this is a tiny minority of the gym population. The best personal trainers have the following,

• Have hired a trainer themselves. They actually believe in and value PT.
• Have a background in movement - doesn't have to be weights, could be gymnastics, tennis, a martial art, etc - in which they've done moderately well over 2+ years. Having moved, they are used to watching movement, and thus understand movement better. This is the beginning of the "coaching eye."
• Have set modestly ambitious physical training goals taking 6+ months to achieve, and achieved them, eg a young woman deadlifting 100kg, a guy running 5km in under 20', either going from healthy bodyfat to sixpack abs, got a black belt in a martial art, rehabilitated an injury requiring surgery, etc. They've done something physically challenging and in which they'll have fallen back along the way (as opposed to the easy newbie gains).
• Some general life experience - other jobs they've been successful at, been married, had children, screwed a few things up, etc. This gives them perspective and empathy which helps them get and keep clients, and get them results.
• Enthusiasm for deeper or broader knowledge of health and fitness, ie they keep studying, including trying out things they think are stupid, so they can have an informed opinion on them. This is quite simply professional development, ie getting better at your job.

Not everyone will have them all, the best will though, and most can be developed over time. There are other things that matter but this will do for a blog post which few will read. 

Think of the trainers you know and ask yourself which of these traits they display. In the US, the number of personal training clients is estimated at 6.4 million; 51.4 million are gym members and 12% or 6.1 million use PT services. That's less than one client per trainer. In Australia, it's estimated that we have twice as many PTs as IT professionals entering the workforce every year. Evidently there are rather a lot of unsuccessful trainers out there. Now consider the above list again and see if you can connect the dots. 

It's easy to get the title "personal trainer". It's not easy to get a job and be good at it.