Why do you think work effectiveness or innovation would drop? The people doing the work already don’t see the profits. Nothing would change for them.
There’s no difference between the board of directors being appointed by investors and then being appointed by elected officials, as far as the employees are concerned.

There’s a difference between a state run and a state owned enterprise.
A publicly owned enterprise is perfectly common, and indistinguishable from any other business.

They’re quite common around the world, and some of the largest companies on the planet are state owned.