For instance, if wages are sticky it may lead to suboptimal real wage movements.The reason why we think inflation is good for solving recessions is we believe it helps to overcome wage stickiness (NGDP, Scott's preferred target, does the same but also has a useful extra effect on the incentives for, and risks of, investment).
In other words, recessions sometimes happen when people are in jobs which are no longer as productive as they used to be (or making products that people don't want so much). In a completely efficient market, their wages would fall, product prices could fall too, some people would move to other jobs and supply and demand would balance at the point of highest output. But in reality it's hard to reduce wages - because of both employment contracts and habit or loss aversion - the psychological defences we build around our current salary level.
So inflation is meant to make this process easier, as a fixed nominal wage is automatically declining in value, at least relative to the prices of all other goods which are rising.
Think of this in a slightly different way. Imagine there were no inflation, but instead all wages did automatically fall. Imagine your contract said that next year's salary would be 3% lower than this year's; with another 3% cut the year after.
Would you just stick around and put up with it? Highly unlikely. You'd either move at the end of the year to somewhere that would match or beat your previous salary; or renegotiate with your boss, which might involve demonstrating that you're more productive or taking on more responsibility. If you couldn't be bothered, then you could stay, but you'd become cheaper and reduce your employer's cost base - letting them reduce product prices and sell more.
Can you imagine a world where that was the default employment contract? It seems far-fetched, but ruthless as it would be, it would encourage people to think more about where and how they could add most value. Without this effect, it's easier to get away with being lazy and ignoring potential opportunities to improve. I am all for people being lazy if they want to, but they should know there's a cost to it - and not just to themselves, but to the rest of the economy too.
In contrast, this entrepreneurial rethinking is exactly the kind of market dynamism that inflation implicitly encourages. Inflation provides a 2-3% subsidy to your efforts to keep yourself competitive. Maybe you don't need that, but look around you. Plenty of people do.