We need to overturn CU if we want to be able to go back to a world where government serves people rather than multinational conglomerates.
It ruled that the federal government was wrong to restrict the speech rights of some groups while allowing other very similar groups to still retain their rights. One of the major examples of this was the media industry. A for-profit newspaper company could spend whatever amount of money it wanted to on political speech. An identical company in a different field could not. This, the court ruled, was unconstitutional.
It also did not grant corporations personhood, the other thing people like to state that it did.
Or we could stop looking at SCOTUS to fix legislation and ask the branch of government who's job it is to fix legislation, Congress.
In practice most of the foxes that promise to do so never actually will.
What's your proposal to solve this?
To me, money in politics is the red herring to keep you from looking at the real election reform that needs to happen, some combination of open primaries (to remove the effect of primaries going to more extreme candidates rather than centrists) and an alternative to first past the post elections to allow people to vote for who they like without worrying about throwing away their votes (there are many different systems to do this, they're all major improvements).
The money in politics is used by the parties to back their preferred candidates and the voters go along with it in the general elections because they don't want to waste their votes. The money helps them do the bad thing but it isn't the bad thing.