That's not much of an issue in practice: to even get a few those ideas implemented already requires voter vigilance and strong societal push.
If you have those then a reliable CPI is just another thing this vigilance/push should cover.
If you don't have them, you wont get far with those proposals either.
So it's not like we can get the proposals into laws, but the CPI will be the issue making them ineffective. It's all or nothing.
Raising taxes and cutting Social Security without getting caught is the third rail of politics. The amount of pressure to find ways to do this is immense.
This is the level of corruption you are dealing with. We are not even on a path from "here" to a place where the CPI is an actual fair estimation of inflation. Most people don't even know this is a problem. It's too complicated for regular folks to even deal with and all the establishment political figures are in on it, so they obviously won't draw attention to it.