AFAIK, there *is* a limit and everything I've heard from the left is that want that, they don't want well-to-do people getting it. The issue is that, if you want the relief to go out fast, you can't do it on a complicated case-by-case basis. You have to just pick a $-number of cash relief per person *and* set a cap on how much an adult can earn and still get it. Anything else is way too complicated to happen anytime soon.
So, you pick a $-number and you pick an income-cap-number, and you do it. The $-number per person is $1400 (which ain't much). The income cap is to be decided. Biden started with an income cap of $150K per person mainly so the opposition could get focused on that and talk him down to a lower number. Last I heard it's $75K income per adult. That's a low cap for people where the cost of living is high, but a high cap in East Bumfrick Iowa. But so it goes. You gotta pick arbitrary things like that or else it will take forever.
And if somebody gets a few bucks too much, well, that's the very least of our problems right now.
I believe there is, but that is another thing the far left is currently up in arms about, along with the $1,400 vs. $2,000; which as I said earlier, I don't mind... $600+$1,400 = $2,000 - I just don't think $2,000, for the people who are truly hurting, is nearly enough, but that's a separate conversation altogether. But the income limit thing - I can't really understand how that's a problem. I think it's pragmatic, responsible and realistic in terms of how you're ever going to get anything done in this climate.