IMO, governments should apply a 2-pronged approach. The first would be a blanket stimulus for those in the lowest income brackets (i.e a monthly or quarterly stimulus check for the bottom 25%.) AND very targeted income relief to the people that actually lost their jobs. (i.e. supplemental unemployment payments) in all but the top 25% income bracket.
This is essentially what I was getting at, a focus on low in one but not every single Penny and of course strong focus on those who lose their job (who become “no income” Individuals at that point.)
All things considered governments did a pretty amazing thing in putting together programs that would usually take 5 years to create and roll out and implemented them in 5 weeks.
That being said, they can make some easy tweaks to improve them going forward.