If the Torah was given on Shavu'ot, wouldn't it be logical to make that day the time to start the reading cycle (or, at least, line up the yearly cycle so I am up to the narrative of matan torah naturally at that time) at that point? Instead, we start and end the cycle on Shmini Atzeret which is not a time which is, as far as I can tell, inherently related to the Torah. This answer quotes a source which posits a possible explanation but nothing definite. This website presents an explanation of sorts but with no sources, and its point is that we should be starting the cycle on Yom Kippur but to avoid some sort of religious confusion, we push off the celebration to what ends up being an arbitrary date.
This explanation, though, devalues Shavu'ot then (or turns it into "Shavuot is therefore more about a relationship with G-d than the Torah itself"). If it isn't about Matan Torah, then why do we celebrate it as "zman matan torateinu"?
When did this cycle timing start and why, and why would we then retain Shavu'ot in its current form, instead of turning it into a spiritual day which ignores the giving of the Torah aspect?