Along with the other comments, theres room for a lot of ways to financially force limits on superheros.
Registration is one thing you mentioned that could require a yearly fee, but you could have extra fees tacked on if they want to actually use their powers. A superhero license that requires a fee, along with training and tests that require fees. The argument being that having a natural talent doesn't mean you have the rights to use it. The education costs could be up there with college loans, leaving them in debt for long periods of time... which the government could "generously" wave if the hero decides to work for the government, with their rules in place. This would give the added issues of heros doing the bidding of evildoers as a matter of survival.
The license could also come with a requirement of liability insurance. Making it very expensive to want to do anything. You could also make requirements regarding any items that they need... supersuits, cars, etc... by only allowing them to be made by government inspected and approved vendors (who could also be in the governments pocket and make subpar equipment that needs to be replaced often.) Vehicles of any sort could require yearly inspections, like smog checks almost... then they would need to pay the inspector, and the fees to license the vehicle, pay state fees for anything really...
You could also impose limits to their power through fines if they speak against the government at all. Get the people on your side for that by saying that their added powers means that imposing their personal beliefs borders on threats... Abuse of power situation. You have to make the heros the enemy of the regular citizenship. If people think that heros are trying to force their own beliefs on them, they are more likely to be leery. Constant speech fines for abuse of power could lead to legal fees... like what happens if you have too many parking tickets...
Do what many dictatorships do and post lists of superheros that have caused harm, even if they stopped someone from getting killed... did they accidentally kill the perps and therefore obstruct justice or interfere with police matters? That's legal fees and bail that can be collected.
Start a "charity" for children whose parents were hurt by superheros. Make them seem out of control and risky... "think about the children". Added benefit to the obvious propaganda, donations from citizens.
As far as taxes, it could be a "peoples relief tax" only applied to registered superheros... or if they are a minor, their families. The fund would be in response to any damages that may occur in a fight situation or just "wear and tear" over some over blown science journal that says something about superheros having a genetic composition that causes more wear on streets and sidewalks (etc.)... it doesn't have to be true.
Regarding the minors and families... a kid's family is going to have to register their child as soon as they realize they have powers, and they will also have to pay that tax regardless of their own abilities. The registration fees for a minor can be higher, as children and teens can be more emotionally erratic. This would put a financial burden on the family that may make them not want to report their child... make it so that if it's found out they lose all property and the child becomes a ward of the state. This could also be a voluntary option for families with limited means, surrendering their child. This would probably be common, as all the financial stress would wear down any family, superheros would be something regular people would dread. As a ward of the state, the young superheros can be groomed however you like.
And getting really dark...There could also develop a type of test for pregnant women to determine if the baby is indeed a superhero or not. The test could be free if you do it voluntarily, and state mandated with a fine if the parents try to get around it. (superhero fraud?) This would lead to people aborting superhero babies... which you could think of a way to spin it "for the greater good" but also make those situations money makers with state approved centers "capable of handling" the -insert derogatory terminology- physiology blah blah
I think the key is to not only make it a burden to the superhero, but to society as a whole. You need your citizens to do some of the work of keeping them down as well. You may wind up with a homeless problem, which you could also work to your advantage as you can spin it as they are inherently worthless and lazy, as there was clearly the option of working for the government. (See, generous) This also may result in a boost in your approval ratings... as you are spinning things to make people believe that you are working in their interests.