You're essentially describing AMD's SEV[1] as mentioned in the article. It piggybacks on the memory encryption implemented in the Zen architecture by giving a separate key for each VM. Ostensibly, the host can't interfere or snoop in the VMs, assuming you trust AMD. I'm surprised it hasn't been more widely adopted.
> protected from anyone except very few who could extract private key from secure chip
The way I understand chip manufacturing it would be hard to diffuse a separate key into each chip. This means it'd only take one of those very few people to extract and leak the key (or cut out the middleman and leak it from inside AMD) to break it for everyone.
> The only real world issue would be side channel attacks.
This is probably a much bigger problem in practice. Spectre & related attacks have been effective against Intel SGX[2], another "trusted environment" inside a larger system.
[1]: https://developer.amd.com/sev/ [2]: https://arstechnica.com/gadgets/2018/08/intels-sgx-blown-wid...