Can bitcoin node startup be secure without validating the entire blockchain? One of the largest hurdles in my mind to increasing the number of full nodes operating is the startup cost related to downloading the blockchain.  A similar but less important (in my mind) issue is the amount of disk space required by the full blockchain.

At Pruning the branches in Merkle Tree Nick ODell writes "[Bitcoin Core] was built on the assumption that you download and validate all blocks."  In Would moving a transaction from an old block to a new one allow more pruning? Murch suggested that some assumptions be checked, and I think one of them was my assumption that it isn't necessary to parse the entire blockchain.  Thanks to Murch, this question is intended to address that assumption.
Full nodes serve several functions on the network:


Validating the blockchain on behalf of their owner
Supplying previous blocks and transactions to other nodes
Relaying transactions and blocks to other nodes


Not validating the blockchain independently sacrifices each of these functions to a degree.


If the node does not independently validate the blockchain, the owner of the full node is still relying on trusting the peer nodes
If the node does not store previous transactions and blocks, it cannot supply them to other nodes that are catching up with the network
If the node hasn't validated the blockchain, it could be tricked into relaying invalid transactions and blocks.


So yes, a node can skip the important step of downloading and validating the blockchain, but I don't think I would consider it to be a "full node" anymore.  It would not be helping the overall network health, nor could it be completely trusted by its owner.  At that point, I would suggest simply running an SPV node.