"Gold Standard era there were many periods of deflation" - yes but that's not so much about inequality.
I think there's a lot merit to Gold is a bit better for equality - but it probably holds us all back in the aggregate.
Elon Musk could not be a Trillionaire in the highly speculative cash-flush situation we have today.
The 2008 crash and the current boom are happening only because of alot of extrea money in the system, and it's going to one group, not the others.
The 2008 bailout was to the 'open secret upper class' aka home owners.
If we 'let the cards fall' in 2008 the banking system would have crashed but it's home prices that would have crashed harder.
A 'stricture monetary system' would have forced people to pay the price. Though it would have had devastating consequences as well - it's possible that with stricter lending, the 2008 crisis would have never happened.
FED sets rates that generally favour the GDP, the growth of which is mostly captured by people with more equity. The more loose money for equity etc the more likely it is to be concentraed.
This is all 100% solvable.
There is no ideological debate needed.
A 'relatively strict' Fed, with rules that favour consumer surplus and that is not fully oriented around equities or some 'outside cause' - that's really truly like 'Gold but with some expansion' ... aka a very small-c conservative approach would be a solution that should be acceptable by pretty much everyone except for the MMT people.
I think it would bode better for 'equality' because money means something known, and large enterprise, financiers can't leverage their influence and scale into making it mean something more for them.