Is it a good idea to make whole theme widgetized?

No technical reason why not to do that , as long as you keep the semantic and code all right (meaning a Header HEAD tag with proper content and footer to accommodate script and functions – both not necessarily visual)
I actually think it is a good idea for a theme …Can give a HUGH flexibility for users , although it would make you need to write widgets to contain ALL the functions of WP , like Content , title, comments etc with a lot of options.
At that point, it is becoming almost a FORK of wordpress 🙂 – But again, +1 for the idea !