I too have been unemployed, and I got less than $348 per week. Given a choice between withholding or not withholding. I chose to not withhold because I'd rather earn interest on that money instead of lending it to the government for free.
My opinion has nothing to do with the extra covid unemployment payments. I'm talking about the smart thing to do with any income where you have the option to withhold or not withhold taxes.
It is always better to receive interest than to loan money to someone for free. Period. If a person doesn't have the willpower to stash that tax money in a savings account, then to thine own self be true and let the government withhold it. But that isn't the smart thing to do.
As far as people with small unemployment checks needing to have the income tax withheld because if they have it in their hand they'll probably spend it instead of saving it: Which is better: to buy food and pay your rent, or to give the government an interest-free loan and go hungry?
Imho it is better to have enough money to pay rent and buy food and pay for other necessities, even if you end up owing more income tax than you can pay and having to pay the relatively low interest rate the IRS charges you for not paying your taxes on time.
To be clear about my intention: When you say "Anyone who is smart about it will have the taxes taken out" what that really means is anyone who doesn't have income tax withheld is being dumb. Well, I am not dumb, and imho it is smarter to not have income tax withheld if you have that option. YMMV