We've been injecting money into the economy in a broad-based way through PPP. It didn't turn out especially well, a lot of it went to large companies that didn't need it, and small businesses (largely restaurants) are going bankrupt in enormous numbers because it didn't help them sufficiently.

You're arguing that a New Deal-esque program is going to be problematic because it's inherently going to have issues in execution, but you're suggesting a solution that there's absolutely no reason to believe won't have issues in execution.