This may be a bit hard for me to explain but I will try...

I think it'd be great to embed a CGS field in a page's template, so that the
value can be changed globally without leaving the page you're on.

It would be sort of what ECB does, but if you change it in one place, it changes
globally. As opposed to ECB's way, which stores the value per page.

It would retain the main purpose of the module, but also make it more efficient
for users to change global values. A field might be related to one page (or two)
but not others, this would be the key difference from modules like ECB.

Example: 
Let's say I have a text field with a value of "October"
Whenever we use {$CustomGS.fieldx} it will still display "October" in our page's
output. But we could have an option to say {$CustomGS.fieldx embed="true"} in
the page's admin we would see an input field where we can change the value from
"October" to "September". And if this CGS is used in other places the value
reflects the change to "September" as well.

Hope this makes sense and wish you will take this in consideration! :-)

thanks!