I am not relaxed anymore but I was for a long time and I think it really just depends on your hair. In general I think not leaving the relaxer on too long is working for people. Whether that leaves you with more of a texturized look or with bone straight hair is what depends on your particular head of hair. My hair always ended up stick straight and my hair grew fine--but I would always rinse just a couple minutes after my mom finished applying the relaxer (usually smoothing the last section more to make sure it was relaxed evenly). But like in baglady's case, I think some people's hair will only get so straight with the relaxer. Leaving the relaxer on longer won't necessarily make it much straighter but it will cause damage just the same.
So to make my point more succintly, I think it's really about the TIME and not necessarily how much curl is left in your hair at the end.
ETA: My general advice is to follow the directions. If you think you could get just as good results with a shorter time then definitely go for it. I don't know anything about texturizing/texlaxing specifically though.