One reason to not use WinEdt:
I can't even imagine writing a serious paper in Portuguese without it.
Example:
latin1: a\c{c}~ao utf8: ação.
I personally type out my LaTeX in WinEdt (screenshots). It's rather a bit easier to use than a notepad-like editor, but many professors talk faster than they (or I) can write. Analysis, in particular, has a tendency to be a bit messy. Either way, even if I had the time to type it out, it would be very hard to follow the professor at the same time. Paper and pencil, in my opinion, is the way to go.