What would happen if the Federal Reserve lost its independence?

First of all, I think all the talk about the Fed losing independence can be ignored. It's not going to happen. The chances are so low that it doesn't even deserve the attention.

But let's say it does happen, what would be the consequences?

Well, pretty much pure chaos. The extent of the damage to the economy cannot even be imagined.

Inflation expectations would de-anchor immediately, even if actual inflation stayed the same. The government would certainly pursue expansionary policies and that would increase inflation.

The US Dollar and US Treasuries would be avoided like the plague. Gold would literally rise "to the moon". The stock market would experience the worst bear market in history. And the great recession and depression would be seen as nice periods in comparison.

The US Congress would never allow this to happen because there's even no way back. There would be always the spectre of this happening again and the damage would be everlasting.