One thing why I see no great benefit in this is that I often use other constructors instead of ->new, for example constructors named ->parse, ->load or ->create - removing that information from the constructor either makes an additional parameter necessary or removes the "gain".

Also, I often create objects through strings/factories, which is unwieldly/impossible with this approach as well:

my $class = "My::App::Plugin::$action";
my $handler = $class->new(...);
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So the slight gain of eliminating ->new isn't worth it to me.