it's a neat idea, but it seems a bit complicated to me.
i have some bones about the markup:
i prefer data-attribs to trying to re-jigger existing attribs.
inline styles are harder to maintain and adjust than CSS.
the init routines look a little too boilerplate-heavy to me.
But, don't think that i am typical at all.
If it works for you and you can build and expand it, go for it.
a widgets is typically a combo of html, css, and js, not just JS.
you CAN use pure JS to build the widgets ui, but it would be a lot more code and harder to maintain than adding behavior to pre-styled HTML chunks.
if you don't need firefox compat, you can store raw html and css in a function's comment block. this lets you keep all three formats in one place and without escaping. Still, most people need firefox, so it gets complicated, and there's no "right" way".
one the one hand, you want all code unescaped for long-term maintenance, greater readability, and text editor suggestions. These assets are usually store together by type, in folders such as /css/ and /js/... On the other hand, you don't want to have to create several files, especially in several different places, each time you add a widget.
Lastly, you don't want to repeat yourself and make each widget a lot heavier than it needs to be. For example, Tabs and Accordions are 90% the same thing, just some behavior adjustments and some different css. It would be nice to be able to add capabilities like "between visit selection persistence" to both widgets from one place. If you had ten widgets in 38 different files, that simple upgrade can be a real chore...
i don't have a perfect solution for you. i would try to build two or three master scripts that provide a framework for making the widgets i need. I think this is how YUI works.
you may want to look into newer copies of dojo: they have a lot of self-contained interaction widgets, and they are now famous for self-loading self-contained widget architecture. I must warn you that AMD modules are probably going to make your head spin at this point; they still give me headaches.
BROWSER STATS [% share]
(2013/10/31) IE7:0.5, IE8:8.6, IE9:5.3, IE10:12.3, FF:17.7, CH:41.8, SF:8.1, MOBILE:20.4