In Segwit, people agreed to put signatures in a separate space called "witness". Why do you think they won't agree to put the whole chain in a separate space (called "archive"?).
Witness is not separate at all. It is an inseparable part of the transaction like any other parts (version, locktime, input count,etc.). Any full node sees this part and fully verifies it (any node that doesn't see or verify it is no longer a full node).
What you are suggesting is eliminating the history meaning the full nodes can no longer verify "everything".