Why does it take 32 ETH to run a node?

The more nodes, the more total message passing between nodes. If a node needs less ETH, more nodes can come online. While this is good for decentralization, it limits Ethereum scalability.

Choosing 32ETH is a compromise, which also comes from a square number, 2 to the 5th power.

Since node messaging is exponential, reducing the validator requirement from 32 ETH to 16 ETH will increase the amount of messaging for all nodes by a factor of 4.

32 was chosen as the minimum amount of ETH staking, which can also yield "finality" in 768 seconds or "2 epochs".