There's no reason to if you specifically block third-party cookies, which is what is being suggested (and what Axios muddies considerably by using "cookie" and "third-party cookie" interchangably).
Unless you're going to throw out local storage and custom request headers, getting rid of cookies isn't really going to do anything except make the same thing less secure (since you won't be able to benefit from the HttpOnly flag).
Unless you're going to throw out local storage and custom request headers, getting rid of cookies isn't really going to do anything except make the same thing less secure (since you won't be able to benefit from the HttpOnly flag).