What’s to prevent one party from forwarding said email chain to any other account on Gmail?

Like most issues of privacy, you can be absolutely perfect but all it takes is any of your contacts to make a common mistake and you are toast.

If a system can only be secure if every participant acts perfectly, and goes through all the hoops required to host their own private infra securely, well, that seems inherently insecure to me.

Email was designed for a different age. All the bolt-on improvements have not fundamentally changed this.