What is the point of a constant (thus known) inflation rate?
As I understand it, your question is the following:

Assuming that the rate is inflation is known by all in advance, does it matter what rate of inflation we set?

The answer to this question is 'yes'. For one thing, even if inflation is predictable, it transfers resources from holders of cash to the government or monetary authority ('seigniorage'). As a result, people may try to hold less cash, which means they need make more trips to the bank (leading to 'shoe leather costs').

Thus, contrary to the supposed lesson of your 'toy model', perfectly predictable inflation can have real effects.

However, you are right to emphasise that the importance of predictability: unpredicted inflation often has effects that predicted inflation does not. For example, consider the common claim that an increase in inflation is good for borrowers and bad for lenders. If unpredicted, that is certainly true. But if predicted by all in advance, one might expect the increase to simply drive up nominal interest rates, leaving the real interest rate unchanged.