You can definitely use "as" in that way to make comparisons, but it is not a very natural way of speaking. Saying "I'm not as tall as my brother" or "I can't run as fast as my friend" sounds much better than creating two separate sentences.

"So" sounds better. "I'm not so tall", or "I can't run so fast".

You now have 4 different answers from 4 different people. I think it sounds perfectly natural and an appropriate use of “as.” Perhaps in different regions, different things sound more natural to different people. I am an American English native speaker that has absolutely no experience in teaching languages. [emoji]

My brother is tall. I am not as tall as he (is). My friend can run fast. I cannot run as fast or I cannot run as fast as him.