Yebbut ........
You've just said "the ideal radial length for ANY ground plane antenna
is slightly longer than 1/4 wavelength, no matter for what frequency". I
assumed that "ideal" = "best".
..
All antennas are a trade off for impedance, bandwidth, gain and in most
cases physical ability to build the structure.
Changing the radial length will have a small effect on impdedance and resonant
point but changing the radial angle will have a bigger effect on impedance
and a very small effect on resonant point.
True - but what's the angle of the radials got to do with their length?
I would suggest downloading the demo version of EZNEC and modeling a GP to
see what small changes in various parameters do.
I had presumed you had already do this (or something similar) in order
to say that slightly longer than a 1/4 wavelength was ideal. However, I
have always assumed that the steeper the angle of the radials, the more
the groundplane becomes like a vertical halfwave dipole - and the lower
becomes the angle of radiation.