[ScaryRacoon]

I would argue that this should be the default behavior for a private tab.

[TazeTSchnitzel]

It seems to be so in Safari.

This can be unhelpful, though, if you need to have multiple tabs open on the same site.

[masklinn]

Yes safari's private browsing goes a bit too far as even opening a new tab from an existing one (e.g. open a link to a new tab/window) isn't linked to the original context. Safari's private browsing also has some issues (e.g. the localStorage quota set to 0)