Interesting thought. Would you be able to put together a test for one of those? pfalls can give you the details for how we expect the test for a new framework to work.
No, they're not. They can run via CGI (so, yes, compiled for each request) but that's slow as ass. They run via Plack/PSGI - they can be deployed in a multitude of ways, including via FastCGI or running standalone using built-in webservers, or via Starman - the latter in particular is very fast indeed. With a simple "hello world" type app, > 6000 requests/sec can be easily handled. Obviously an app of more realistic complexity won't be quite that fast, but you'll still handle many requests every second with no trouble. http://stackoverflow.com/a/4770406/4040 contains some basic benchmarks.
EDIT: also, mod_perl is generally best avoided these days; it's old, not very pleasant to work with, and ties you to Apache. Writing an app with Dancer / Mojolicious etc means you can deploy in various different ways with ease.
"Oh, they're just frameworks for CGI/Perl and thus severely crippled by CGI's mode" - This isn't true.
Dancer use PSGI (not CGI) and most modern Perl webapp frameworks (Mojo & Catalyst) use PSGI/Plack (http://plackperl.org/). The PSGI model is very similar to wsgi which allows for different types of persistent servers.
