Edited for snark removal.
Thinking is not "answering questions".
In order to build a mental model of a problem, you need a rather good model of the environment in your mind, and this comes from memory and the habit of thinking (which is what drill exercises facilitate).
Rote learning is an essential tool in being able to create adequate models of the environment.
The problem is lots of people think it is useless because "I did not need to memorize", when the issue is that "they are sufficiently able to memorize that they do it unconsciously". But most people need to put the effort.
Unless things have changed in the 30+ years since I was in college, I seem to recall exams happen after weeks of study and not "on demand". Part of learning is memorization. There's no way around that. It sounds more like you aren't cut out for the pace of high-caliber institutions which move very quickly. I have two friends with literature degrees, one from UCONN and one from Dartmouth. The Dartmouth friend had to read 4x the number of books than the UCONN friend in the same period of time for the same degree. C-students still need jobs! Just because you aren't a straight-A doesn't mean you can't still be a serviceable employee.
The need to manually solve the formulas has since been superceded by basic calculators. But it's still all (personal opinion) unnecessary rote equation solving these days. I certainly could've used more emphasis on structure and less on longhand math.
Good to know it's the same over there!