I think there may be some confusion here. All of the BMS's we have been talking about - and almost all BMS's on the market - are "common port" meaning that both the load (discharge) and charge go through the same port. So you can't "only use a contactor for the load side". If the contactor cuts off the load, it also cuts off the charging.
MOSFET-based BMS's generally can separately control charging and discharging, because there are separate directional MOSFET circuits set up for each of the two current directions - In and out of the battery. A contactor is not directional, so either both charge and discharge are ON, or they are both OFF.