Consider, why not double-wrap your stream? Put TLS on top of TLS on top of HTTP?
You can see this pro-HTTPS opinion all over this discussion.
As for your "consider", I personally do double-wrap many streams: I have a VPN for my browser. The VPN is great for hiding my home traffic from being spied on by my ISP. Without the VPN, HTTPS streams would reveal hostnames (SNI) and IP addresses to my ISP.
If it's the exact same implementation then that doesn't really add a second layer. If, however, I am provided the option to run HTTPS over a VPN tunnel, then I would happily do that in a heartbeat. In fact, I frequently do run my web traffic over a proxy, thereby giving it at least two layers of encryption.
Do you have a response to my question? "Consider, why not double-wrap your stream? Put TLS on top of TLS on top of HTTP?"
Double-encrypting something with the same technique is pretty much always a sign of cargo cult crypto. Modern ciphers, like those used by TLS, are strong enough that there’s no reasonable way to break them applied once, and the downside is that applying them twice is making things slower than they need to be for zero added benefit.
On the other hand, TLS and PGP are very different things serving very different purposes, so nesting those makes sense. There is an added benefit from TLS, namely that you ensure that everything is protected in transit - including the HTTP protocol itself (which is currently not protected and which might be subject to manipulation as shown in this post). Plus, it provides some resistance to eavesdropping (and with eSNI + mirrors hosted on shared hosts, that resistance should improve further).
Sorry I don’t understand what double wrapping has to do with it, or why you’d ever do that.