I can definitely understand how that might be useful in some cases, but I think there might be complications that could make it difficult to implement. For instance it would only be useful for very specific project configurations, so it could be difficult to generalize enough to be useful in the Editor as a whole. We may be able to come up with some sort of behavior that might be suitable, however, so thanks for the suggestion. Don’t forget to vote for it!
As a workaround in the meantime, if you turn off auto-refresh and open a tab to the file you’re working on, it will stay there and you can manually refresh it. There’s also an existing request at Refresh App on Changes to make auto-refresh not take you back to the homepage that might be of interest to you.