Your old toilet was probably calcified which had nothing to do with the piping. A toilet will flush, and maybe flush better, without a vent. A power flush pushed the material out of the toilet "faster", but once the material is in the pipes it doesn't make any difference what kind of toilet you had. The Toto may be the "best of the best", but I have only installed about 8 of them in all the years I have been installing toilets. I have not had any customers complain about the function of the ones I do use, either.