It was annoying to setup, and technically complicated, but it worked.
If 3rd party cookies had never been enabled, that's what we would be doing today, and you would never even know your traffic was being sent to a 3rd party.
There's a reason they enabled 3rd party cookies: Because blocking them did not help at all.
Today such proxying would be even easier. Don't promote banning 3rd party cookies, you'll just make privacy even worse.