First, I can tell that you've never experienced poverty in your life because saying it's 'as simple as that' ignores the times when poor people need to purchase something right away. They deposit a check into their account, then go shopping because that money SHOULD BE IN THEIR ACCOUNT and they desperately need things like food or basic amenities. Then they get pinged with overdraft fees because the bank decided not to cash that check right away, instead delaying it so they can collect overdraft fees.
As for your second point, calling 'profit and productivity irrelevant' is ridiculously flippant because profit and productivity doesn't come from the void. It's generated by people. So let me illustrate:
Person A is 'creating' $1000/year in value.
Person B is 'short' $300/year in order to survive.
Person A employs Person B. The reason why Person B is short of funds is because Person A is earning their value from Person B and not properly distributing that wealth down through labor to Person B. Ergo, the situation isn't some sort of 'wealth transfer', it's the result of someone not being fairly compensated for their work.
What you're calling 'wealth transfer' is the result of money accumulating towards the top, which results in the wealthy having to either pay more to support the bottom percent or let them die. Software engineers generate many more times their income in value to the companies that employ them. Which means money floats to the top as companies try to depress wages to maximize profit margins.