If the problem is the web, then the problem should be addressed by the web, not TLS.
...and of course, part of the problem is that we've conflated nearly everything to the "web", so thinking that the web is somehow removed from this problem is a mistake.
> We eavesdrop your purchase, we were prevented from tampering with it. But, this is the Web. The eavesdropped TLS session contains a secret cookie value, which identifies you to Amazon. We can use this to impersonate you and do whatever we want, just as if we were able to tamper with your TLS session. The apparently more limited permissions are a mirage.
Yup, that's a legit problem, though I'd argue it actually further reinforces my point. This is a good example of a problem that stems from conflating multiple security concerns, rather than addressing them as separate concerns.
If there's an acknowledgement that your authenticated & tamper proof session is fully exposed to eaves dropping, then you start using the authentication mechanism itself to identify people or you develop an additional identification mechanism that is resilient to replay attacks (both of which are entirely possible) or people just inherently become aware of the reality that buying stuff on Amazon from an eavesdropping environment means that they will be impersonated on Amazon. What you don't do is think a "secret cookie value" is a secret when it so clearly is not.
But it's essential in practice to remember that overwhelmingly the environment people are interested in is the Web, and on the Web those aren't actually different things again, in practice.
For example, suppose you're OK with me eavesdropping your Amazon purchases. You're buying a Lego robot for your daughter's birthday, you work for the investment bank, it's nice that we even let you do that from work and clearly we can't just let you do whatever you want with no oversight or you might rob us blind. We have a hypothetical TLS 1.4 which lets you opt in to this eavesdropping but nothing else, and you've done exactly this.
We eavesdrop your purchase, we were prevented from tampering with it. But, this is the Web. The eavesdropped TLS session contains a secret cookie value, which identifies you to Amazon. We can use this to impersonate you and do whatever we want, just as if we were able to tamper with your TLS session. The apparently more limited permissions are a mirage.