Not according to Armstrong. He says that you can even use a #4.5 with up to 30" radius curves.
#4.5 22" RCR, 36" SR
#5 26" RCR, 44" SR
Basically, he argues that #6 and #8 turnouts are space wasters on model railroads, especially with radii of 24" or less. Other than the comment regarding #4.5 turnouts and 30" radius, he really doesn't address broad curves (his definition of 30" radius and greater in HO) directly.
His most basic point seems to be this: The radius of the closure rail (RCR) will affect how "stiff" eqipment like steam locos will negotiate the turnout, and the substitution radius (SR) will affect the train as a whole.
BTW, he argues for laying your own track and building curved turnouts when needed. He diagrams how that saves space.
He does argue for higher numbered turnouts in reverse (S) curves for other reasons, which he discusses at length in another section of the book.