There is no cperldoc-mode in the web, did you mean perldoc.el ?

Or do you mean:  cperl-perldoc or cperl-perldoc-at-point¹ ?

(I occasionally use  M-x woman)

I suppose the benefit from info-files comes from better highlighting, being able to navigate with hyperlinks and using a search over all documents, I'm afraid cperl-perldoc can't do this.

UPDATES/FOOTNOTES:

(1) They work fine, but like always the keybindings are ridiculously long C-c C-h p or C-c C-h P, thankfully they can be redefined...

REPLY TO YOUR UPDATE:

> perl-perldoc-at-point was what you meant

No, cperl-info-on-command and  cperl-info-on-current-command was what I meant. 8)

and cperl-perldoc-at-point was what you meant! ;-)