It's interesting to model this sort of arrangement, note the wide
range of feedpoint impedances that will be seen on the different
bands, and observe the feedline losses that might be incurred when it
is directly fed with 50 ohm coax. If you then introduce an ideal
transformer at the feedpoint and repeat the exercise you will
generally find that feedline losses increase on some bands and
decrease on others.

With the vertical length I tried, the effect of a 1:9 transformer was
to limit the more extreme losses at the cost of making some very low
losses higher. I guess over the several bands I tried you could say
there was a net improvement with the transformer.

But one question would be how to build this ideal 1:9 transformer
which maintains its transformation ratio and exhibits zero loss across
the wide range of impedances and frequencies involved.

Steve G3TXQ