I thought players would want more money per year the longer the contract
Yes and no. There are a lot of factors at play however most I will skip because I don't think your too interested and they aren't in play here. A typical contract is a contract where the team and player agree to a certain amount of money paid over a certain time with the amount agreed upon spread out evenly over the duration of the contract. For example 20 million over 5 years which means 4 million per year. Thus in terms of once a contract is signed a player will not be getting more money.