Inflation (as measured by the CPI) measures price changes. Wage indexes measure wage changes.
You want to measure both separately so you can do exactly the kinds of comparisons you want to do above ("Hypothetically, let's say the CPI indicates that prices are double what they were ten years ago. Is the median consumer better or worse off? Who knows! Maybe wages are the same as they were ten years ago, and everything takes twice as much work to acquire. Maybe wages have tripled in that time and goods seem cheap.")
Money supply is measured separately since it affects lots of other things too (eg, the relationship between interest rates and money supply). You have to measure all these things separately because that lets you tease apart the relationships.
Again, if the OP is talking about increases in money supply (which I agree can lead to increases in the speculative assets) then you need to explain how buying silver would protect against those increases (since the silver price is uncorrelated with those speculative increases).
You want to measure both separately so you can do exactly the kinds of comparisons you want to do above ("Hypothetically, let's say the CPI indicates that prices are double what they were ten years ago. Is the median consumer better or worse off? Who knows! Maybe wages are the same as they were ten years ago, and everything takes twice as much work to acquire. Maybe wages have tripled in that time and goods seem cheap.")
Money supply is measured separately since it affects lots of other things too (eg, the relationship between interest rates and money supply). You have to measure all these things separately because that lets you tease apart the relationships.
Again, if the OP is talking about increases in money supply (which I agree can lead to increases in the speculative assets) then you need to explain how buying silver would protect against those increases (since the silver price is uncorrelated with those speculative increases).