I work on a team of 6 devs that use this process and I can attest that it works wonders. At all my previous companies we used agile and it's remarkably slower than the "squeaky wheel process".

As long as there's trust, accountability, and a sense of ownership by everyone on the team, you don't need a structured process to be effective. It just slows everything down.

You could probably even scale this to larger companies by keeping team sizes small and have managers be the "squeakers".