As a Personal Trainer, here is my take:
For most, a CPT is as much as anything, a motivational tool when one knows they have trouble doing the things that they need or want to do to become healthier on their own. You pay money, you schedule times to meet and that can serve to make one feel compelled to show up and do the work. In other words, it creates a level of commitment b/c you paid and scheduled it. It creates accountability, b/c you have to show up or call to cancel or if you forget, will get a call or text from the trainer "where r you?". As time goes on and that person finds a way to stay motivated even without a trainer, they may go it alone.
For a select few, a trainer/coach is necessary to push them in more advanced athletic endeavors, from contests and competitions (body building and power lifting) to sports performance. Here is when you hire a much more specialized coach. And many times, it can be the difference from placing 5th and 1st, depending on the coach as they handle more then "showing up and working out." They program, manage the program and adjust, handle the nutrition plan and adjust and help out with all the other details.
Obviously, you fit into the first description, and it is up to you. If you think you can stay consistent with you training and nutrition (the biggest issue most people have is consistency), then you probably do not. But remember that you do probably need guidance of some form. Follow a person or company that gives you info, guidance and troubleshooting to help you either design a program or buy a program, template, find and use one of the many free apps and programs online etc. The key is following a good program, not just "showing up" to "exercise". Know what you are going to do today. Be smart enough to know how to adjust when things change (you're not recovered yet in the area you want to train, the machines/stations/benches are all taken up and you don't have time to wait so what can you replace an exercise with, etc). These things are what helps people the most. Same point with nutrition. Find a good app to log your nutrition. Plan your meals. And there is a wealth of free info out there to show you how to track and plan meals for your week. Do these and you may not need a hired trainer.