While true, this only works if you are assuming that the block is valid. To verify that the block is valid, you actually need the entire history of the blockcha

While true, this only works if you are assuming that the block is valid. To verify that the block is valid, you actually need the entire history of the blockchain, including processing yourself every single transaction that has ever been made over the blockchain. What you describe is SPV verification, which basically says "if a miner decided to spend $10,000 in electricity mining this block, they probably verified the transactions first, so I probably don't need to verify it myself". Of course, if everyone makes this assumption, it's very easy for the miners to start slipping in illegal transactions without anyone noticing. So, some of the network running SPV is okay, but too much is a great systemic risk.