You'd still be leaking through dns (and basically all non-http communication) and applications which don't adhere to proxy settings, which are a lot. Webrtc doesn't go through the proxy either iirc

Also, you're still trusting Amazon to play by the rules, which is unlikely if state actors are involved as the comment (which spawned this discussion) insinuated

It's educational to try.

I had to tunnel dns through openvpn to make dnssec reliable.

On a wifi router, there's loads of leakage; mdns, ntp, things devices do to check for captive portal, weather apps, etc etc.

You can mitm https, but breaks hsts sites, unless you hack your browser