Obviously inflation for no benefit is still bad, but if we were to say print a little money and use it to pay entry level public sector way more than entry level private sector, I wouldn't complain. Shatter the illusion that rich people can stay rich without doing anything impressive. And add some inheritance tax too, if we wanted dynasties in the US we'd have been goddamn loyalists, what are you? British?
Printing money doesn't produce wealth though. Printing money only works in the long run if it encourages new production that otherwise would not have occurred.
Also, "new production" only helps the masses if they are somehow part owners in the enterprises that are making that new production, so it's not even as simple as that.
If you want to break "the rich can stay rich without doing anything" you need to advocate capital gains taxes higher than income taxes and/or other means that make it easier for labor to buy capital than for capital to buy more capital. Basically we need a way to make more people owners of capital so they can reap its rewards, rather than making it more and more difficult for people who don't currently own capital to gain some.
This is the heart of UBI discussions - how to spread the benefit of society's improvements in productivity back to the masses rather than to just the owners. I think the word 'socialism' is a bogeyman here; there are likely ways you can do this without having state ownership of all companies. For instance, all pay packages could be required to include equity, not just salary. You could have zero income tax and only tax capital gain (yes you may dampen the amount of risk-taking because of this, but you won't eliminate it completely). There are probably other ways to do this that I'm too limited to devise.