So, am I the only one who still uses tubes in my tires on a high quality carbon frame bike? I haven't looked at new wheels or tires for some time and all I see now are tubeless. I'm not a racer, but a serious senior enthusiast. I'm having extreme difficulty getting Conti 4000s tires/tubes on and off my Reynolds Attack wheels. I needed two sets of pliers and four levers to get the tire off. After 30 minutes of exhaustion, I'm not putting them back on. So thinking of new wheels, unless another tire/tube will be easier to install on my wheels, which are still fine really. Maybe the well in the rim is too shallow? or the kevlar bead is just too small?
You are definitely not the only one. I'm using tubes in all of my road oriented bikes (anything in the 25mm-32mm range).
I'm also a little surprised to hear you are having trouble with Conti 4000s. I've used those for years and have been able to mount them by hand on many different wheels.
I've recently picked up two sets of Hunt carbon wheels. They are a newer brand, based in the UK, but their wheels are fantastic, decently priced, and I've had no problems mounting Conti GP4000 and GP5000 tires on them. The added bonus is many models are in stock or set to ship in the very near future.
One thing you definitely want to be careful of if you are sticking to tubes is to stay away from 'hookless' rims. They are generally considered tubeless only, and they are notoriously difficult to mount tires on. Enve and a few other brands have jumped into hookless with both feet. Some brands are still making hooked rims (Hunt being one of them), so look for those.
