Indexing it keeps it at EXACTLY the same effective level as it is now. (Technically, it would be slightly LESS of a problem every year. Indexing it to wage growth would keep it EXACTLY even with where it is today. Inflation has historically been lower than wage growth.)
This is NOT like SS. SS is a problem because ALL of the money collected for it was wasted instead of being invested.
Indexing might make it slightly LESS a continuing problem at the bottom, but MW is not really about the bottom wage, but about the 'bracket creep' it serves to create. In that case, the law of unintended consequences of indexing MW to inflation would be to tag more and more salaries to that index, meaning each yearly index adjustment artificially raises many more salaries, and the level of inflation such salaries create. It would also serve to truncate other types of annual raises, meaning salaries based on communist principles (I deserve a salary/raise for breathing)and not rewards for effective labor.