Here is where it gets complicated. Societies that have used gold to measure wealth, went in conquest to destroy other nations in order to aquire the wealth.

One could argue that with gold, you would never be able to run deficits since your paper currency would be backed by equal gold.

The problem here is that when money is needed, it would be very difficult to get since you have to go and find ways to aquire more gold. If I was Microsoft and needed to grow to the next level but I didn't have 20 billion to fund a new project, then I would need to wage war, or spend an extraordinary amount of time to find investors.

This is where fiat shines.

When it comes to full scale governments, their abuse of fiat is what causes inflation.

It is possible that if bad actors did not exist, then fiat could expand the money supply as needed and reduced as needed to avoid inflation. But this is not the case because government spends more than they can generate. That's what throws the balance off.

While you are 100% correct that inflation makes the rich richer, it isn't any different with gold. The real difference is in who the actors are. Those who had gold alway acted to get more. And they will go to great lengths to source it, even if it means traveling across the ocean to destroy another civilization. Again not that fiat hasn't also caused this, it's just the actors taking advantage of the system.