Should Kolmogorov complexity include all resources or just program size?
Should Kc be restated as being resource based and not solely program size based?


No.  If you change the definition like that, you get a different concept, and the different concepts deserves its own different name.  If you want to examine that concept, you should give it its own name.  Kolmogorov complexity is a standard term with an accepting meaning; trying to "change" its meaning would only cause confusion.

Instead, if you want to study that alternative concept, give it a new name, and then study its properties.  There's no need to change the existing definition of Kolmogorov complexity: Kolmogorov complexity is an interesting and useful concept to have in one's vocabulary.  Removing it from our mental toolbox would only make our intellectual scope poorer.

To give you an analogy: If curves of the form $y=ax^2+bx+c$ are more useful in a practical application than lines, should we re-define the term "linear" to mean a function that can be expressed as $y=ax^2+bx+c$?  No, that would only cause confusion.  Instead, we give a different name (quadratic) to the different concept.