I believe that is a dangerous misrepresentation of history and current regulatory constraints. They had a very basic angle-of-attack indicator on their first airplane. In fact it was their only flight instrument. There should be no implication that they felt they could fly entirely by the seat of their pants. They did not trust their abilities that much, so it seems unwise for anyone else to be too trusting of their abilities except where exceptional circumstances require it.
Since the FAA regulations do not require an AoA indicator, but do require an airspeed indicator, the only alternative we later pilots seem to have is to use the airspeed indicator and keep the bank angle shallow so that the airspeed indicator can be used as a crude replacement for the AoA indicator.
With respect to the original bank angle question, here is a specific recommendation from an AOPA ASF stall/spin safety article:
"Don’t exceed 30 degrees of bank in the traffic pattern."
http://www.aopa.org/asf/publications/topics/stall_spin.pdf
From the FAA stall and spin AC:
"Excessively steep banks should be avoided because the airplane will stall at a much higher speed."
http://www.mccc.edu/~kuhlj/classpix/AVI 132/AC 61-67c stall spin.pdf