German taxes are really horrible, in general. They expect you to pay in advance for expected untaxed income (based on the previous year's return). Working out the taxes on the income from some ETF is a nightmare, unless your platform does it for you. Unless you really understand the system and can file your own taxes, then low-wage freelance work just doesn't make sense as the cost of doing the taxes can be higher than your income. This means people are trapped into not working.
You can negotiate to have your advances reduced but the government really doesn't like it when businesses (including freelancers and solo entrepreneurs) have a high difference between their advances and the actual taxes. This also goes for declaring your VAT (which depending on how much you make you'll have to do monthly or quarterly as an advance and then alongside your income tax) and while in that case you basically set the advance yourself you'll get in trouble if it doesn't match your actual VAT (difference between charged and paid).
You can file your own taxes and if you're a regular employee there are tons of non-commercial orgs you can go to that will assist you in doing that but if you're a "business" (even if it's just you and you haven't incorporated) they'll often not help you.
BTW the reason you can just forego filing your own taxes as an employee if you just want to be taxed on your wages (and don't have anything else to declare, e.g. interest on savings) is that your employer already had to do the taxes on your wages and benefits for you. So it's not like the government just does them themselves, it's just done by payroll instead of you.
Now, with the 300 Euros of fuel relief, every employee will have to file taxes on said 300 Euros.