Yes, it would have been unfair and yet still fairer to the individuals. The system we have benefitted a bunch of business owners more than it did individuals.

I'm not saying that the current system was good, but I don't think your solution helps at all given that it doesn't help those who need it but hands out truckloads of cash to those who don't. There's zero reason to give a huge payment to someone who wasn't in financial distress and who probably never even lost their job. As has been mentioned Canada's CERB, which was a "if you say you need it we'll give you some money now and we can sort it out later" approach helped the poorest the same as the more well off, which makes a lot more sense.

I agree that a refund of income taxes alone is not a good solution. I was thinking we should have also given money to those who did not pay any federal income taxes, just as we are doing with unemployment benefits now.

We could also have capped the size of the refund.

Regardless, I still think giving money directly to individuals is much better than PPP. PPP was offered because it benefitted banks and existing businesses, who have more political power than the poor.