Exactly the opposite: CPI is worse than the alternatives at long timescales, despite their flaws.
I know you really really want to make this about the flaws in the alternatives, but I have spent many sentences dealing with the flaws in those in good faith while you have yet to reciprocate at all with any in defense of CPI, either in comparative or absolute terms. Because you know that's a losing game. CPI is cooked, the FRED real wages graph is cooked, your conclusion from it is cooked, and you know it's cooked.
I know you really really want to make this about the flaws in the alternatives, but I have spent many sentences dealing with the flaws in those in good faith while you have yet to reciprocate at all with any in defense of CPI, either in comparative or absolute terms. Because you know that's a losing game. CPI is cooked, the FRED real wages graph is cooked, your conclusion from it is cooked, and you know it's cooked.