Any means testing that isn't basically automatic will tend to exclude the people who are unable to leap over the hurdles. You know, the people who most need it. The "basically automatic" way of means testing involves having the IRS use the tax returns and bank information it has on file. It doesn't have everyone's bank information (though they can mail checks too), and for the first round of checks they had the problem that not everyone had yet filed for 2019. So "eligibility" for a pandemic relief in 2020 depended on income in 2019 or 2018. This was stupid then, but at least it was right at the beginning. It's absolute nonsense now, as your 2019 income says nothing about how the pandemic in 2020 has impacted you.
There's a simpler way to means test, if you must, which is just taxing some of it back later, but all these brain geniuses don't like that for reasons. The reasons are they don't like the whole idea at all. Better to boost banker bonuses so they can hire more servants, or something.
But assuming any of these people are operating in good faith, that brings us back to stupid. Maybe "we" didn't think of all of these complications months ago, but they're well understood by anyone who has paid any attention to things at all. Economists are going to economist. No need to educate themselves about practical issues.