YES. Exactly.
Just a small correction: The balancing mechanism is to "switch on" small surface-mounted resistors (with PWM using FETs) to keep the cells that reach 4.20 volts from exceeding that voltage. The current to the whole pack is restricted during this phase by the power limits on...
Chargers with an adjustable endpoint are already available in the aftermarket for 48 and 52-volt packs. It is a very cheap and easy analog solution, but the circuits must be accessible to install an adjustment pot.
These Luna Charger 48V Advanced 300W Ebike Charger also have an adjustable...
This sounds like the BMS is balancing the cell groups, but maybe going too far.
But def a BMS problem and not the charger. Chargers are relatively stupid devices. The BMS is where the "intelligence" is.