> But hoarding wealth isn't a problem for inequality.
It absolutely can be, especially for wealth that is finite. (Like land for housing)
> Inflation is the process that incentivizes capital to be put to work.
Does it though? Inflation mostly just punishes labor alone, labor feels the effects of inflation far more severely than anyone else.
With enough capital (the amount anyone 'hoarding wealth' already has), the capital automatically buys itself out of any problem of inflation, because the returns to sit on that cash are routinely higher than inflation itself is.
Inflation can't currently incentivize capital to be put to work, because capital just sitting doing nothing already far out-earns any loss from inflation. And for inflation to be strong enough to actually incentivize capital to be used, you'd have to bump it to astronomical heights (like say, 15-25%), at which point you've completely obliterated all wage-earning people's lives.
This is why many well-respected people advocate for a wealth tax. In a perfect world, inflation would be exactly 0, and a strong punitive wealth tax would discourage greedy people from hoarding wealth.