The fundamental question: Are radio waves a simple electric waves or the
very sophisticated Maxwell's waves?

ALL radio waves can be described by maxwell's equations, both simple
linear polarized ones and circularly polarized ones.

The fundamental question is really how can we describe this "wave".? A
wave of what "water",
A wave of "water" traveling towards a beach.
Is it water we are really trying to describe or what?
Water has a "skin" on its surface , a skin that encasulates it like a
bag , container or a boundary!
Nothing is clear when describing a "wave" with respect to physics, as
it is just a "F" word to substitute an unexplainable in a psuedo
description
There is no agreement what so ever as to what a "wave" is so there
cannot exist a description of what radio "IS", "IS"!. Physicists
acknowledge that radio is some thing that is unexplanable leaving just
hams to fill in the unexplainable about radio and to deny the
explanations made by others.
What we do have is a string of mathematical equations all of which
interlock which are a result
of observation and seamingly reasonable deductions. Maxwell deduced b
y examination of units used that a portion of his formula was also a
mathematical explanation of elevation and acceleration but no
description of what! A physicists
named Gauss who provided a lot of Maxwells tools
used Newtons laws to establish boundary laws where it can be seen that
mathematically a clump of static particles in equilibrium could be
made
dynamic by adding a time varying field while retaining equilibrium
meshes with Maxwells equations on radiation. So who on earth descided
to interject "waves" into the discussion and why?
And what experiment was performed that dictated its inclusion in the
subject of radio or radiation that has put a screaming halt to a
sustainable explanation of same for more than a hundred years
where other dreams have come to fruition by utelizing the human brain.
Is it the ham population
that is responsible for the lack of advances in the advancement of
science by denying the inclusion of particles as the basic matter
involved in elevation and acceleration (displacement) as implied by
Maxwell's equations, preferring instead to use 'water' and 'waves' to
describe the science to the non initiated.