What's the advantage of making a new node sync from the genesis block?
The great advantage of a new node starting from the genesis block is that the node is able to individually verify every transaction is valid and does not need to trust any other node to know that when done the entire blockchain is valid. The blockchain is verified independently and the integrity of the blockchain is established.

For those not interested in that, it is possible to just run an SPV client which just uses the headers.