The economic view would be something like:
- There's a pie to be split, often beforehand. Some players are in better negotiating positions than others. Sadly, if you don't know a lot of performers, you'll have a hard time getting a bigger slice from the one that shows up.
- It's not actually relevant who is on the document as a "writer". This is simply a thing to be negotiated over so that the performer is incentivized to do the recording. It's the same thing as putting up sales tax on a purchaser of goods, legally the buyer is paying x% extra, but economically the buyer and the seller actually split the bill according to negotiating power.
- What will happen if it's enshrined that only the person who actually wrote the piece gets his name on it? Well there will be other things to bargain over. For instance, maybe you get your name exclusively on the song, but you put it in a company and the performer gets a piece of the company.