I once worked at a place that basically just used perl server side. In this decade (2010s). The codebase was just one tangled mess.
They told a story of a guy who failed the cultural interview because he told a VP "you can't write a large web app in perl", and of course they had done just that. With the reflection of hind sight I think despite the obvious empirical counter factual, he was on to something. It really was an uphill battle against the language to do things large scale.
It's not impossible, it's a cultural mismatch. Perl is obscenely permissive, which makes it a really interesting and weird language.
But when you work in a big team and make something complex, you want something that's consistent. All of that permissiveness and flexibility bites you.
Now, with good styling guides and linting, you can make it work for complex software with a big team, but that's culturally pretty anti-perl. We're trying to do that with Javascript now, which isn't as weird as perl, but has many of the same excesses that you want to reign in with a style guide.
In my company we primarily use Perl, but it's just on my team for our ETL pipeline. It works really well, especially since we modernized our older code and enforced really tight code standards. To use Perl end to end, well, there are modules for that (such as Dancer), but I can't comment on them because I've never had to use them.
I recommend Dancer, actually Dancer2 now. So easy to write web apps. Maintainable ones too! Most of the basics of app security are covered within the framework. And where there are gaps (like CSRF tokens), it's trivial to add primitives via DSL.
I tend to answer "can you...?" questions by pointing out that you can do just about anything in any Turing-complete language. The more useful questions are whether you should, and if not, why not. It sounds like an annoying hair-splitting technical distinction, but I've found it leads to more useful discussions.
I think developers have moved on to reinventing Perl in JavaScript. Ever since I saw "use strict"; in a .js file my eyes have not stopped rolling. Personally, I'd choose Perl over JavaScript, Python or Ruby any day of the week but I'd lose all my hipster cred.
Java is in the same boat, but at least it's still marketable so engineers don't mind working with it as much.