Apart from not actually 'matching' the impedance you are correct (although it can of course be used that way). It is commonly called, and even listed as, a matching transformer. However it's usually used to tap power off a line rather than 'match' the power, in exactly the same way as a mains transformer for an ELV 10W bulb.Very easy to understand (albeit there are several different ways of 'looking at it'). However, unlike your microphone transformer scenario, in this case one usually will want to use an (impedance) 'matching transformer', since one wants to optimise power transfer to the speaker.
Fair enough but you are only talking about how one marks the transformer, not what it is doing (which always is 'matching' the source impedance to the speaker impedance, to optimise power transfer) - the only important thing being that the 'power' figures specified only apply to a particular voltage (which I will assume is 100V RMS at full power) (and which I might have expected would be indicated on the transformer!).
Once one knows the source voltage at a particular maximum power, it is arithmetically trivial to determine what source impedance it equates to, and hence what impedance ratio (hence also turns/voltage ratio) is required to 'match' the source impedance to any given speaker impedance.
Assuming 100V RMS at full power (and also assuming I can do arithmetically correct in the middle of the night!), the following tabulation shows that for the example you illustrated. In other words, marking the transformer with powers (with an assumed voltage) and speaker impedances is just one way of doing it. The same information would still all be there if the transformer were specified in terms of turns, voltage or impedance ratios - but perhaps some of those who use them would not be capable of understanding that?
View attachment 280533
Kind Regards, John
100V output amplifiers are rarely run into a matched loudspeaker load.
I've blocked out the information in your chart that is not required or considered or useful in 99.99999999999% of applications of such a device and as you say; not even understood by a very high percentage of the installers of such a device.
Some of that information may come on a data sheet with the transformer or a device containing it
or may even be printed on a device containing one
But the reality is in the main the the only 'really useful' information is the power.
As you say the calculations are trivial and similar to some I do on a regular basis for bespoke situations