If Perl 6 had been presented from the start as an experimental 'sister language' (perhaps with a different name), rather than being named as Perl 5's successor over a decade early, perhaps the perception would now be different.
People express that sentiment often, but I've never found it realistic. Many of the philosophical goals of Perl 6 are the same philosophical goals Larry had when designing Perl 5. Many of the tactical approaches are far different, but there's where my disagreement with the "It deserved the label as an experiment at the time!" idea arises. No one really knew how far redesigning Perl needed to go to achieve those philosophical goals until the RFCs and Apocalypses started pulling at loose strings in the sweater.
Isn't your term 'Modern Perl' itself a way of saying that things have changed a bit since 1993, even though we're still using 'Perl 5'?
Certainly, though it's less about using new and exciting features because they're new and exciting than it is about understanding how the language and its features, both new and old do—and, in some cases, don't—work. The biggest and most important language change has been the gradual lexicalizing of features such as filehandles, pragmas, grammar modifications, and even packages. You may have to squint to see the latter, but it's there. Perl 6 takes that principle to another level.