That will make the context switch back to the original product easier to do.
I would like to suggest that this becomes a priority, at least from a developer standpoint. I’m not an administrator for a large deployment so cannot comment on how impactful this change will be where. Context switching from even from tab to tab is killing your productivity if you need to think on every switch. If the switch is effortless then the productivity hit is far smaller.
In terms of ideas you could look into sending additional contextual information with the new tab being opened. Like the source site name and product. This could then be used on the admin site page to assist with followup actions like installing an app. The install app dialog could then pre-fill the site/product to install the app on or could ask the user if the action is meant for the site they make from.
Maybe getting to solution specific but I see easy low hanging fruit solutions to overcome the context switching frustrations.
Also to reiterate @remie point, why was this not an RFC?