That is indeed the way that all small transformers are rated. Our standard “EU” a.c. adapter is rated at 230 V in, 9.0 V ±5% out, the open-circuit voltage is 11.5 V ±5%.
That should result in less distortion, because it will reduce the flux in the transformer core. I believe we don’t do it because it’s perceived as a waste of energy.
I did, quite a long while ago, test a similar 400 V transformer on 240 V, and it was not noticeably better in the degree of waveform distortion compared to our standard a.c. adapter, which surprised me. I suspect the reason is such small transformers are designed for the minimum possible size, and waveform purity and losses are not a consideration.
If you have a computer and sound card, you could use the method described in the a.c. adapter test report in the ‘Learn’ section. The spreadsheet (or rather, instructions to make it) is here: ZMPT101B, powerfactor and current shown - #52 by Robert.Wall
It is set up for checking the phase error. If you do that, please note the warnings in that and subsequent posts, and be VERY, VERY careful if you connect to the mains side. If you’re only interested in the distortion components, then you need only use one channel on the low voltage side, and that should be relatively safe. But you still need to make sure do don’t destroy your sound card with too much voltage applied to its inputs.
You change the harmonic number in cell K3 N2 and compare the amplitude and phase of each harmonic with the fundamental (1).