Why do master nodes need to store EVERY block and not just the last, say, 100?

It just seems like a hassle for a new master node to download so much data in order to host the blockchain. I understand why it is necessary for atleast a few nodes to have the full blockchain so people can still view information on early blocks, but it just seems like a restriction that discourages new users from wanting their own master node.

If blocks are truly dependent on the hash from the previous block, then just a chain of 2-3 seems plenty tamper proof on its own. Why doesn't ethereum have some sort of method of letting people just download a bunch of the most recent blocks and that's good enough?