The One True Way of Training

Yours is not the One True Way, nor is theirs. There is no One True Perfect Routine, it depends on the capabilities and goals of the individual. 

For some, low-rep strength work will be best. For others, circuit will be best. For others still, something else. Deal with the individual person. What's the first word in our job title? Personal. 

As well, there's room in the industry for a lot of different approaches to training. At a previous gym I worked at, the two most successful trainers had very different approaches to training. One was all the bosu ball stuff, the other had the people running around puffing like a steam engine. If they swapped clients, in a week half of them would be gone - the people have chosen that PT as their trainer because they like that style. But the clients of each both get good results, and stay with them. Me, I was the third most successful one there and rising, and I have a different style again.

The diversity of styles is a strength, not a weakness. There is no One True Perfect Routine, clients need to be able to choose from a variety to suit their own personality; but at the same time, we as trainers need to have a broad view and see what we can take from others' styles.

The best routine is the one you stick to. If your clients are not returning, then your routine is no good (but see below). Compromise and be patient. Better an okay routine they stick to than a "perfect" routine they quit after one session. As well, communicate. There should be a rational reason for every exercise, every rep and every set, and you should be able to explain this to the client. Once they understand why they're balancing on a bosu ball or squatting deep or whatever, they will be more motivated to do it - and perhaps come back after the first session.

Lastly, remember that you are dealing mostly with beginners, and for beginners, it doesn't really matter what they do. For the first 6-12 weeks anything at all is going to improve them all-round. Just using the treadmill will improve their strength, just doing barbell squats will improve their cardiovascular endurance, and so on. They were doing nothing before, now they are doing something, something is more than nothing, so they improve. 

So even if there were One True Perfect Routine eventually, there isn't for the first 6-12 weeks. This gives you time to ease them into your particular style of training. 

I'm reminded of a story a client told me. She'd told a previous trainer that she wanted to get stronger, and she had 2x 1/2 hr sessions a week. He told her that because she needed 2'00" rest between sets, she needed a full hour, anything less was pointless, and she had to warmup and cooldown. And of course there were warmup sets too. So she was doing about 3 work sets in half an hour session, and spending a lot of time sitting around doing nothing. This is why he is her former trainer.

I told her, "Look, would it be better to have more time? Sure. Give me 4 hours a day 6 days a week and in two months you'll be built like Jessica Biel in Blade Trinity. But does this mean half an hour a couple of times a week is useless? No. We can still do useful stuff. Your progress would be quicker with longer and more frequent sessions, but you will still progress." 

The woman started off squatting 30kg and struggled to put a 20kg barbell overhead. The exact sets and reps and rest are not that important for her, she just needs practice lifting heavy shit.  12 months later she squatted 70kg and pressed 30kg. Would she have progressed faster if we had more time each week? Undoubtedly. But with less time she still progressed 

He was impatient and uncompromising, so she ditched him as a trainer. I was patient and compromised, so now she has increased session frequency; for the first six months she was once per week, after that twice, nowadays she does three a week, and is still with me after 18 months. Sometimes the route to your destination is not a straight line.
On the other hand: While the client's being injured or failing to return shows that your routine is probably no good, the client's uninjured return does not mean it is good. Maybe they just like you, or don't know any better. There is no One True Way, but there are many many Bad Ways.