Unemployment is not the only economic measure. Basically what you're advocating is fighting misleading claims by politicians by creating your own, even more misleading (at least the politicians talk about unemployment when they say "unemployment") metrics which makes even harder for the voter to understand what is going on because it mixes a half-dozen of different societal problems into one number.

> if you look at the "true" unemployment, i.e., what that voter is thinking, which is how poor are Americans overall

Unemployment is not a measure how poor people are. While unemployment can lead to poverty, it's not the same as poverty. It's like saying "we'll add a number of sick people, obese people, people not working out, old people, people eating too much sugar, people not eating enough vegetables, people who smoke and people who drink alcohol - and call it 'true health index' and will demand to treat this number as if all these people were actually sick". Somehow you think it's more clear this way?

> well you'd actually see a pretty glooming picture with a large number of Americans living below poverty

There already are statistical measures of poverty. You don't need to call them "true unemployment". Call them "measures of poverty".