This must be some weird difference between our setups, since I do not get any kind of Chrome freeze with that on either Linux or Windows.

Maybe if you launch Chrome with a completely fresh profile (without any plugins), something different shows up?

use File::Temp 'tempdir';
my $mech = WWW::Mechanize::Chrome->new(
    headless => 0,
    data_directory => tempdir(CLEANUP => 1 ),
    launch_arg => [ " --enable-logging", "--v=1" ]
);
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