Meanwell PB-1200-12? That is a 60A charger.
you do need a charger, since that does go into float once the batteries are full. A power supply doesn't. You can use a PSU to charge, but need to manually stop charging.
What do you call a high end BMS? I haven't seen BMSses which are actually chargers and thus lowering voltage. A BMS is the last line of defense, and does cutoff if the thresholds are reached, but it's not intended to act as a charger or whatever.
Also, keep in mind most powersupplies are 12V, and can't be adjusted to 14V. You want like 14V in order for the balancer to work as well. Charging with 12V isn't going to do much
Server PSU's generally can be modified to output higher voltages, but 14V+ is requiring to disable/modifiy the OVP as well.
Also, I'm not fully sure if they have CC so actually CAN be used as a charger.
Better get a 15V powersupply and dail it down, it's more easy to get 14-14.2V than 'upgrading' from a 12V.