It seem to me a web app like this enables a re-think of the file and sheets organizational structure, which is really a compromise due to the limitations of a local file based application. It's simulating being able to link different spreadsheets together by putting them all in the same file.

For a web app, linking to other independent sheets should be the way to go. You'd need a convenient way to define links to other sheets (perhaps defining an alias for links to the other sheet), browse linked sheets and open them in another browser tab. Browsers already have multiple tabs, so there's no need to have a tab based structure for this inside a browser tab.

Just throwing it out there, I've not thought the consequences through really, but it seems a shame to just blindly recreate a file based metaphor.