Cutoff should be $125k income per household and below. That's twice the median US household income. Anyone who makes more than that should not be getting a check.
I'm in the bracket above that and we are responsible savers with a mortgage and a kiddo on the way. We don't need help and live life responsibly below our means
It's a hard line to draw. Everyone's financial situation is different. AGI is probably the best indicator of wealth for this purpose but at the same time it's not always indicative of disposable income. There are expenses that people incur that can't be deducted for purposes of AGI. I imagine there are plenty of people who show income over $125k, don't live extravagantly and will still need some help to make ends meet.
I'm not sure there's a right answer.