The
measured radiation resistance can be as high as 5000 ohms or as low as
2 or 3 ohms..."

yep..

That's why I wonder about the popularity of these 9-to-1 baluns.

generally a waste of money I think... Some bands they might
help, some might hurt... The reason I think it's a waste of time
is rarely are they actually needed to improve the s/n ratio.

One of my antennas is a 20 meter end fed wire, and I tune it with an
old Heathkit AC-1 antenna tuner, which is made especially for random
length, end fed wires. A modern equivalent would be something like the
MFJ-16010 random wire tuner, which at $49.95 doesn't cost much more
than some of the 9-1 baluns I see advertised :-)

I've had one of those 16010's since about 1978. Still works, and I
usually use for a mobile impedance matcher. You can reverse the
leads if you want to match a low z load vs the normal high Z used
with most random wire tuners.

It would require bringing the random wire into your residence, and
then running a short length of coax from the tuner to the receiver. I
understand some wouldn't like that because of in-house noise, but
there are always trade-offs to anything.

Myself, giving that there is usually no increase in s/n ratio
when using a tuner to match a random wire, or other wire
antenna, I'd generally prefer a preselector over a tuner.
The tuner will help reduce out of band signals, but the
preselector will usually do a better job at that.
You can make a simple random wire tuner with a wound
coil that you can tap with a gator clip, and a variable cap.
The 16010 uses a wound tapped toroid inductor instead of the
coil, but otherwise is the same.
When listening on 160m with my IC 706mk2g, I sometimes
get AM-BC interference that puts images across the band.
We have a lot of strong MW stations in this town.
Using my MFJ-989c T match tuner will clean that stuff
right up. So even a tuner will act as a preselector of sorts.
MK