Yes I cannot agree more. Personally this shift in people's expectations of Private Browsing or Incognito Browsing came in a way that felt sudden. The recent lawsuit about Google tracking you in Incognito mode was absolutely dumbfounding to me: of course websites can still track you! If only people still remembered the origins of this feature in 2005 (or 2008 in Chrome's case). But even on HN the opinion was pretty split. It is indeed clear that it is now time to change what private browsing means.
However, I don't think this is going to stay this way for long. The word "private" when it comes to computing has many varied definitions and it all depends on who the information is made private to. In the extreme case, if your threat model is privacy from eavesdroppers on the network or the ISP, then a browser can easily claim any HTTPS connection is private enough; the majority of browsing is already private browsing. If it is privacy from others using the same machine, then this older private browsing already works. But I cannot help but feel that a few years down the road people are going to consciously or subconsciously substitute yet another definition of privacy.