Show me any device on earth that can run a browser that has no proprietary code whatsoever (including hardware) on it?

AFAIK older Talos Secure Workstation with Power CPUs was it. Everything open including CPU firmware.

Not sure about smartphones though - they mostly struggle with a fact there are no truly open source baseband.

There is no smartphone fully powered by open firmware. Also keep in mind that the hardware itself is proprietary too.