On top of what you said about the effect of printing making valuations high, only temporarily and only on paper, the opposite lack of printing, is actual redistribution towards the rich in a much more real and persistent way.
Insufficiently inflationary money can be used as a way for the rich to withdraw from the private economy when things are getting too turbulent and park their wealth in government paper having greater than market rates of returns (on a risk adjusted, liquidity adjusted basis). If government money didn't exist, these people would have to stay in the turbulence when the economy hits a storm.
In a private economy, it's normal for returns on assets to occasionally turn negative. Wealth is sometimes difficult to keep constantly growing year after year. With low inflation, the rich can divest from private assets at the first sign of trouble, shrink or close businesses, kick employees to the curb and they get to park their wealth in government guaranteed paper. A deflationary government currency is basically a subsidy for causing unemployment and destroying careers, a subsidy that often gets indirectly paid by the poor. Money printer keep going brrr please.