I suspect that you will be quite surprised at the lack of tap roots in your roses. A vigorous fibrous root system is the norm for woody plants. It's how they absorb water, dissolved elements, oxygen, and how they stay PUT in the ground!

One reason for repotting is to replace the collapsed potting medium, which after 3 years will have lost many of the physical properties crucial to healthy (container grown) plants. And unless you are building a very strong, coarse medium that can stand up to 3 years of culture, you can expect muck in a year! Select your ingredients with care.

Any of the plants that I have grown for long periods of time in containers thrive after root pruning. As a matter of fact, they thrive BECAUSE of it, and I consider it an essential aspect of long term container culture. I have not grown roses in containers, however.

You might want to post this question in the Rose Forum, too, for added input.