Jakob Bauer wrote:

Is it actually still called a high brace then?

Yes - the name is based on the position of the paddle relative to the forearm -
if the paddle is below the forearm, it's a low brace; if above, it's a high brace.

I seem to meet about the same number of
people who tell me that I should stay well clear of the high brace
(e.g., William Not Bill Nealy), as of those who tell me that it's
essential to have

A poorly done high brace is a risk - the "old" way of doing it was to get your
elbows up and extend the arms; this put the shoulder at risk. Properly done,
the "new" way keeps the elbows down and keeps the shoulder joint closed and
better protected. Those who say not to do it are referring to the old technique.

The high brace is just too important to ignore.

Mike