In the current system, we’ve shown we can generate inflation when we need to.

We can sometimes generate inflation. After the GFC, the US and Europe had a hard time following the playbook you outlined. In Europe, deflation set in but central banks couldn't drop rates below zero (at least not every effectively). Europe stimulated but not very much and fairly quickly pivoted to austerity measures, particularly for Southern Europe. Those countries did not fare well and took about a decade to recover to pre-crisis GDP. This lead to secondary problems like rise of populism. The lesson is that you don't want to start off with rates too near zero when a downturn comes, because then you can't lower them.

The US fared better, but the initial stimulus packed was clearly too small, and we also had an austerity contingent in Congress who wanted the opposite of stimulus. So our downturn was longer than it needed to be. I agree with you that we can generate inflation (within limits) but that doesn't mean government officials will act when they need to.

Mungofitch mentioned that inflation allows companies to reduce payroll without cutting wages, which is hard to do. There is another way to cut payroll, and that is to reduce headcount. So if a little bit of inflation prevents some layoffs, that's a good thing. So that 2% target rate is doing some heavy lifting.