Prove same origin
A cross-site form gets your cookies automatically, so cookies alone do not prove the request is yours. A CSRF token is a secret the attacker's page cannot read, required in the request body. That is the proof.
SameSite is a floor
SameSite=Lax/Strict stops the browser from sending the cookie cross-site, closing most cases. It is not the whole answer for top-level navigations or older browsers, so keep the token for state-changing requests.