Still I hear more times szklanki, kieliszka if used in such sentence than szklankę mleka:
It sounds very strange to me and I've never ever heard this, I can't even imagine that any Polish speaker could say so. But I may be wrong, after all, people are making the weirdest kinds of mistakes. Could it be regional?
Unless you mean negative sentences, then it's ok - nie napijesz się szklanki mleka.
Strzyga. However, you must know that it is very common to say "wypij sobie kielicha" or "napij się kielicha" or "chlapnij sobie kielicha". No one at their common senses, that is before any drinking, will ever say "wypij sobie kielich".
You're right, of course, but it's limited to kielich od wódka :) Would you say that "wypij sobie szklanki herbaty" sounds as good?