Adequate inflation is also a sign of a growing economy. In Japan's case, Japan had full employment for over 20 years and they had no inflation for over 40 years. So no, I don't think curbing potential mass-unemployment was in their reasoning when they had decided to start QE in 2016.
> Inflation allows companies to effectively cut everyone's wages by x% instead of firing x% of workers.
I guess? but only because inflation often is related weaker currency, which increases export (making companies richer). This works for export-led economies like SK and Japan but their export growths are slowing down.
> So the question is 1. are they right that there would be large scale layoffs absent the inflation? and 2. Is it better for everyone to get a pay cut or some people to get laid off?
Well you already have your answer. There has been no mass layoffs absent inflation for a long time.
and most central banks are small and most currencies/economies are a lot more vulnerable to exchange rate changes.
because when an economic downturn starts in export oriented smaller economies the following happens. the reversal of a lot of capital/money flows (investment projects put on hold, sovereign and corporate bond market slows/halts), and then as a consequence of this exchange rate drops (the currency of the smaller economy depreciates) ... and at the same time, basically as the other side of this is that everyone buys US assets (reverse flow!), which pushes up the price of the dollar, which is an extra problem for developing economies, makes raising new debt a big problem (servicing rollover debt is a must at least, and developing economies want to outgrow their debt, so they have a high debt load usually), makes everything instantly more expensive.
central banks act as dampers, and there are a bunch of papers about profitability of them, and they detail that by them buying assets when they are undervalued and selling when they are overvalued is their way to dampen these swings and make a profit. which in some cases gets sent to the government budget (eg. in case of Mexico).
so yes, while there are asset bubbles that are a consequence of low interest rates, they are not the purpose, nor they are the main consequence of low interest rates, the main effect is economic growth, which helps to lower unemployment, and to avoid recessions (which easily leads to an unemployment spiral).