That's a great suggestion! I used the 'User-Agent Switcher' add-on [1] and that seems to have done the trick for both the websites I reported above. (edit: I chose the option 'Windows / Chrome 146' in the add-on's UI).
As someone else said here, we should probably chalk it up to laziness on developers' part; maybe there's more to it, but I'll take that explanation and move on :-)
[1]: https://addons.mozilla.org/en-US/firefox/addon/uaswitcher/