It could well be that CentOS excluded CPAN.pm on purpose too hamper such installations!

Searching CentOs How to install CPAN modules¹ directly leads to a page stating

If your system is one of the most popular Linux distributions then by far the easiest way to install additional CPAN modules is to use the package management system.

For distributions like RedHat, CentOS, Fedora, Mandriva etc most CPAN libraries are available as RPM packages. If you need a CPAN library called CGI::Session then the naming convention normally used is perl-CGI-Session. ...

IMHO changing system Perl (IF REALLY necessary) should always be done with a package manager, cause they are meant to allow clean and easy rollbacks. (dunno how far the guaranty goes)

On all accounts your recommendation of perlbrew for an alternative private installation is surely preferable!

¹) which is just the threadtitle + OS, shouldn't be too difficult...