Near-monies show wealth; the more wealth people contain, the more they are likely to spend of current income. Also, the fact that near-monies are liquid adds to potential economic instability. People might cash in their near-monies & spend the proceeds whereas the monetary authorities are attempting to stem inflation through reducing the money supply. At last, near-monies can complex monetary policy since M1, M2, M2+, and M2++ do not always change in the similar direction.
The argument for involving non-chequable savings deposits in a description of money is that saving deposits can rapidly be transferred to a chequing account or withdrawn as cash & spent.