We've discussed this before, but I think you are vastly overestimating how much money will actually be inherited by the working class...

... it won't be much at all.

The assets owned by the working class boomers will be spent on themselves... boomers will live 20/30 years past retirement so that eats up a ton of their wealth, and then medical expenses will essentially eat up the rest. Their kids won't inherit much, and the most likely scenario is that their kids will have to look after them in their last years as they run out of money.

For the majority, they'll have to financially look after their kids and their parents.

The vast majority of the wealth (I dunno, 90%) will be inherited by already wealthy families that won't sell off the properties or stocks. It'll be hoarded and not flow through the economy at all. You are absolutely right that the billionaires will grow in wealth over time, unless proper tax reform (ie, closing loopholes) are implemented.

Inflation will still rise, but not because of inherited wealth, but because of corporate capture of policy.