It would be nice to see all of the bases in my vault and quickly jump to them.
Proposed solution
Currently there is a “Properties” tab for viewing and editing the properties across your vault. Same thing with a “Tags” tab. It would be nice if there were also a “Bases” tab.
When you open your-base.base and drag that window to a side tab, its formulas apply to the active note (which is what I think you mean by “main view”; the active note changes when you click on another note).
When you embed ![[your-base.base]] in a note or use a base code block and drag that note to a side tab, its formulas apply to that note (and doesn’t change even when you click other notes).