> why /shouldn't/ we make the change?

It breaks doctests, and probably some other unit tests, too, e.g. for output formatting.

What should we suggest users to do? Replace

    >>> get_flag(…)
    <app_enums.TrickyFlag: 1>

by

    >>> get_flag(…) == app_enums.TrickyFlag  or get_flag(…)  # (also show result on failure)
    True

and

    assertEqual(
        "You caught the %s flag!" % result,
        "You caught the app_enums.TrickyFlag flag!")

by

    assertEqual(
        ("You caught the %s flag!" % result).replace("app_enums.", ""),
        "You caught the TrickyFlag flag!")

?

Note that using "%r" does not help, since it's also backwards incompatible.

For their own enums, users can probably backport (or forward-port) "__str__()" and "__repr__()" themselves in order to work around this difference. But it's something they would have to do.

I certainly understand the reasoning, and it also makes new Py3.10-only doctests nicer, actually, but IMHO it counts as deliberate breakage.