I definitely agree with you w/r to "strict function order." I think the ordering is OK if one doesn't define ordering as "in order of strength/skill/cognizance". I think there are plenty of people whose auxiliary is there, but disfavored, e.g., a very Ti-ish INFJ shows lots of Ni, and is very Ti-logical, but the Te or Fe rarely seems to appear. That is to say, ordering can help define the overall type in such a way to point out areas for growth. But no, the ordering doesn't tell you which function is "strongest" or "weakest".
This and your previosu statement make me qestion whether you even use Ti or an introverted Te or understand the quality of Ti that a Ti person would. I like the way you phrased Ti-Logical with a qualifier. Would be like me being an Fi-Feeler. It adds a detachment or what you refer to as lack of quality.
edit: this is meant from a strictly Ti stand point and not an attack.