Wages are a key inflation driver; IAMW would be a perpetual motion inflation engine.
Long term, if you have MW as a key minimum support measure, you want it to keep pace or better with inflation, but over the short term you want it to be countercyclical with inflation, rising most rapidly when inflation is low, and least when it is high.
And this leaves out discussion of the problems of a minimum wage as a basic support mechanism, which are also significant.
We could plausibly tie it to targeted inflation (or just have it rise on a fixed schedule). We shouldn't tie it to measured or anticipated inflation, for the reasons you say.
Long term, if you have MW as a key minimum support measure, you want it to keep pace or better with inflation, but over the short term you want it to be countercyclical with inflation, rising most rapidly when inflation is low, and least when it is high.
And this leaves out discussion of the problems of a minimum wage as a basic support mechanism, which are also significant.