As a personal trainer, I also didn't find a use for percentages. When it's just me and one client, I'm able to accurately figure out how they are performing and can vary the weights appropriately given the desired training effect. This is a form of auto-regulation, even though I'm doing it for someone else.
My time at BU has helped me to find an appropriate time and place for percentage based stuff, though. With a team of college athletes percentages is the easiest way to go about making sure everyone is working at the appropriate difficulty. You'll always have the athletes who want to go HAM on the weights regardless of the fact that their spine looks like a big question mark. You'll also always have the athletes that are uber-lazy and will load themselves at 50% of their capability. Providing them with a specific number takes away all that guesswork.
You can also, more often than not, accurately guess how a college athlete is going to be feeling at a given time. Given the schedule of their season and their academic year, you know when they will be feeling shitty and run down and when they will be feeling strong. Too, since many of them have a pretty young training age you will often be able to get good results using a slightly more conservative percentage than you might for yourself.
Percentage based programming isn't guesswork. Alexander Sergeyvitch Prileprin created a chart that was based off of a ton of research done with Russian Olympic weightlifters. This chart has become a part of the famed "Russian Texts" (texts like books, not text messages) that so many great coaches have based their training off of. Louie Simmons of Westside Barbell has really championed this chart for many years with his powerlifters. Recently Rudy Nielson of The Outlaw Way has applied this concept to programming that reaches a wide variety of lifters. Jim Wendler's 5/3/1 is possibly the most well-known application of percentages (while not necessarily a direct application of Prileprins work).
So, percentage based programming isn't for everyone. It would drive me crazy right now, but I'm sure there will be a time in the future where it will work perfectly for me. Consider it for yourself, and if you have any questions please ask in the comments section!
Have a great day, and go lift some heavy shit!