First, intertemporal comparisons may be of academic use, but economic actors can only decide between good a and good b contemporaneously; you can't choose between buying good a today and buying it last year.
True, but as you point out, you can choose between buying a good now and buying it a year from now. To predict the future price you need to be able to analyze past prices and understand the reasons for the changes.
It does matter when it is possible to choose between a good today and a good tomorrow, such as deciding whether to make a particular investment. But for low risk goods, where the rate of inflation will meaningfully affect real returns, they are typically liquid enough that the market appropriately prices in the expected inflation...
The market only factors in price inflation. You're still left with malinvestments which looked profitable on paper, even after factoring in price inflation, but are actually net losses because they are below the average real rate of return and draw resources away from other, more profitable ventures. Yes, investors should be looking to get the highest possible return for their money, but not everyone can find above-average investments, and for those who can't, inflation leads them to invest somewhere to avoid the inflationary loss even if the economy would be better off with them simply holding on to their money.
And for high risk ventures, whether the payoff is 50% or -50% is going to be determined by the success or failure of the risk, not the movement of the medium of account.
True, but only if you're talking about the actual payoff after the fact rather than the expected payoff prior to investing, and it's the latter which determines whether or not you choose to invest. Changes in the money supply affect all investments near the margin, whether low risk or high risk.
Lastly, a little money illusion can be a good thing.... The best example is unemployment. It is generally better for ten people to take a 10% real paycut than for 1 out of 10 to lose a job while the others keep their original pay.... Some inflation allows for real pay cuts in response to real supply shocks while mitigating the baseline anchoring bias.
Yes, that was one of the original arguments for inflation. It was an underhanded trick to begin with, playing on the average worker's supposed ignorance of basic economics to fool them into accepting lower pay than they thought they'd been promised. Well, that only works so long as your employees remain ignorant of inflation, which is a necessarily transient state. The workers figured out this little scheme and fought back by demanding inflation-indexed wages.