Whether it is permitted or not permitted, anyone who opens a sefer to learn during any part of davening is making the statement that they would rather be doing anything, but, davening.
Well, on Shabbos/Yom Tov, I sometimes find myself waiting by Shochen Ad/Hakel before the Chazzan gets there. In those cases, I’ll open a sefer – and I don’t think it makes the statement you claim it does.
Ditto for the time between which I finish Shomeneh Esrei and C”H begins (at which point I promptly close the sefer).
The Wolf