That raises the question - why bother taking those people's money in the first place?

Well, you're not taking those people's money in the first place. The justification for including them in both calculations is so that there are no discontinuities in the system where producing a little more of value for others means taking home a lot less in resources for yourself (like many means-tested programs).

One time a year payments (tax returns) have a different spending pattern than many times a year payments (welfare programs, and pension programs). The second pattern is the one that sustains people at the bottom edge of wealth. The former is what causes extra consumption.

Additionally, poor people live in areas with literally no banks.

Both of those alone justify a monthly payment method.

the argument is because that translates to tax credits, which basically means the exact system we have right now that everybody wants to scrap. So clearly we can't do that.