CKKS is a levelled scheme, because the rescale $\lfloor\frac{x}{\Delta}\rceil$ operation requires truncating a modulus to be efficiently evaluated, and rescale is (usually) needed after every multiplication to control noise growth.
But I don't understand why rescale have to decrease ciphertext modulus. In residue number system it is probably hard to divide without removing ciphertext modulus, but would it be right that under (integer) high precision arithmetic system, we just have to naively divide each coefficient of ciphertext with $\Delta$ (with integer division), hence achieving FHE without need of bootstrapping?
Thanks.