This is already the case. Except this solution eliminates a lot of the existing opportunities for corruption by generally simplifying the model.
> There will absolutely be people who abuse the system and use this money to not cover their required expenses and use it for a variety of things they don't need.
It's a thousand bucks- pretty hard to live large on 1k. Besides, comparing the issue of poor people abusing handouts to corporate welfare is molehills to mountains. If your concern is abuse having a detrimental impact on the society as a whole, don't look at poor people.