In the sense I think you might mean, nothing
should be done. I use Perl 5, I like Perl 5. I don't see a need to regard static unparsability as a problem and "solve" it. Larry apparently is going to static parsability in Perl 6. I don't have a firm opinion about whether that is bad or good. I do think that it's proved wise in the past to listen to Larry in these matters.
The reason for a proof is there had been considerable question about whether Perl 5 was statically unparsable just for practical purposes, or just given present parsing techniques. Adam Kennedy's PPI man page says that the module name Parse::Perl had been reserved in case someone invented a way to statically parse Perl. Opinion shifted to the point where the most people felt certain that no static parser for Perl existed. But I think it's nice to get the issue completely nailed down.
Lack of static parsability is an obstacle for many utilities that deal with Perl 5 code. That's definitely a downside. But it's not the whole equation, and the ability to do Turing-equivalent fiddling at BEGIN time is an upside.