Breakage could be a big problem, especially when you go to wear your hair out and the natural part is thick, whereas the relaxed/texturized part is a great deal thinner, so when you wear your hair out, it just doesn't look right. In addition, it is hard to comb your hair and not cause damage if the roots are super thick and the ends are not as thick.
Although my hair was texturized, I got tired of looking at it because it looked so thin and sickly compared to my dark and thick new growth. From comparing the textures, I really could see what chemicals had done to my hair. Even though I always assumed my texturized looked a lot like my natural hair, seeing both textures together, I could see that a change had taken place with my hair.