I'm going to use the Code Review community as an example, but it works for several others as well:
When we are seeing a question on stackoverflow and we click on the icon on the top left side, we are redirected to the main page (https://stackoverflow.com/) of this community, perfect, as I believe it should be:
However, in Code Review for example as we have the habit of clicking on this icon from this position to return to the main page of the community, it actually indicates a visit to the StackExchange, making this work difficult:
My tip is that to keep the community standard, this top left icon change the logo to Code Review and when clicked takes you directly to the Code Review home page (https://codereview.stackexchange.com/).