Mathematically it wouldn’t do much but it would make people feel more invested I suspect.
Fun fact: the US Treasury accepts donations to pay down the debt: https://www.treasurydirect.gov/govt/reports/pd/gift/gift.htm
You can also donate to the general fund: https://www.fiscal.treasury.gov/public/gifts-to-government.h...
If some guy walks into your government office and says he'll give you ten million dollars to increase everyones' salaries, but only if you arrest all the homeless people on his street, you just created a perverse incentive. You can claim that anti-bribery laws fix this, but it's a who watches the watcher problem. To be clear, regular government has this problem too in the form of political donations and lobbying, but removing even the thin veneer of legitimacy that our current taxation system has (where you can't opt out of paying for social safety nets or into specific initiatives) makes open bribery almost inevitable.
Meanwhile if you earn $1M/month, then it's absolutely trivial to live in a way that $100K more or less makes no practical difference.
Or if you do odd jobs and managed to scrounge up $100, you now have to do the paperwork to pay the $10 you owe, which seems like an odd thing for a government to bother with taking care of and enforcing.
Now here comes the logical thought of "what if we set a minimum", and you have the beginnings of tax brackets.
Mathematically, this is equivalent to a small UBI.
Or vice versa. UBI requires lots of people to implement it. A simpler income tax rate doesn't.
What's nice about it is you could basically just get paid post-tax from every income source, and they all know to subtract 10%, and the government would just need a simple web portal for you to claim back your first 25k.