Methinks an antenna is just one part of an antenna "system" and that it
doesn't
need to be resonant.

and you are basically correct. an antenna is 'resonant' at only specific
frequencies, even a small bit away from those frequencies it goes out of
resonance but performance is virtually unchanged... if this weren't true the
venerable 1/2 wave dipole and 1/4 wave verticals would only work on a single
frequency... so we know from experience that you don't have to have an
exactly resonant antenna.

note above i said 'frequencies'. this is to account of course for the
resonances at multiples of the lowest resonant frequency.

likewise you can operate an antenna well away from it's resonances and it
will still 'work'... theoretically an infinitely small dipole will radiate a
field only a couple db weaker than a 1/2 wave dipole in free space... with
the difference being that the 1/2 wave dipole changes the shape of the
doughnut a bit, thus creating stronger fields in some directions and weaker
ones in other directions. keep raising the frequency so that an antenna is
longer and longer as measured in wavelengths and the pattern of these fields
changes, but the total radiated power remains the same... so you can say
that any antenna 'works' at any frequency and be correct.

The kicker comes when you start considering the whole system. while any
antenna will radiate whatever power you get into it (minus a bit for
resistance of the elements that gets lost as heat), the problem can be
getting that power to go into it in the first place. this is where the
'resonant' antenna does help out. at resonance an antenna presents a purely
resistive impedance to the feed line, generally this is a relatively easy
load to push power into.... except of course in extreme cases of very low or
very high impedances. as such it simplifies the requirements for the
feedline and transmitter.

if a transmitter doesn't have to handle highly reactive loads, or extremely
high or low impedances, it can be made much simpler and from easier to build
or buy parts. if you have to design a transmitter to power a highly
reactive load you have to be able to handle higher voltages or currents...
higher voltages mean wider capacitor spacings, more insulation, and higher
dielectric losses.. higher currents mean thicker conductors or expensive
plating to lower resistance, and higher resistive losses.. both of those
losses mean that in order to create the same radiated field intensity you
need to generate more power in the transmitter to get it through the feed
system to the antenna where it can be radiate. so while the antenna will
radiate whatever you can give it, just getting it there in the first place
can be a chore.