It just sounded like you assumed the charger itself had to lower its output when its output dropping is just a byproduct. "your bms will not allow that 5.3kW at the top" "4.6kW sounds like a lot at 99%". multiplying the constant charge current by the maximum voltage of the battery is a good quick check of peak charging power, and it seemed that you took that for 99%=~116V while charging.
I don't know elcon's general programming specifically, but I know at some point it is basically a CC/CV charger with extra protections hopefully based on best practices. CC/CV is pretty simple--it just describes two limits while charging and how it approaches them. Most power supplies that have a current limit and adjustable voltage are already capable of CC/CV, albeit with possible overshoot.
If you want a fully charged battery at 116V (or so), 116V would be your CV setting. If you pick a certain rate in amps (say 30 amps) to charge that your charger and battery are capable of (wiring, bms, contactor, cells, etc.) this would be your CC setting, or limit. To push this current, the charger switches "on and off" and dumps charge very rapidly, effectively "setting" a voltage output. This voltage output is of course still tied from charger to battery terminals so the power that is coming out is only a slight voltage differential along the power wires from the battery voltage, with lots of current. Even though you set it to output 116V, the current is too low to maintain that voltage while charging the battery. By monitoring and carefully controlling that rapid switching, the voltage differential is varied and causes ONLY enough current so that it does not surpass your 30Amp CC limit. If at any point the voltage reaches the set CV limit, the charger is still rapidly switching--but only to maintain that voltage now, and no higher. As this goes on the battery is depositing charge and the current begins to lower because the voltage differential is smaller because the switching duty cycle doesn't need to be as high to maintain that voltage. Switching between CC and CV is more or less automatic as they are both limits. Some chargers may bounce between CC and CV a few times (typically lower quality) when hitting their limits, and they may overshoot their CV target in tiny pulses. That being said, by design I believe diginow's elcons "bounce" and reduce their power level (by lowering voltage which causes lower current) a few times when approaching full and I'm told this has something to do with balancing.
Ideally it would pay attention to charger, battery cell, and ambient temperature (to reduce the charging rate), balance (to give the BMS whatever conditions it can best balance at before reaching CV and stop charging in an emergency if one cell rises too fast), voltage lift while charging (to see if the battery is even hooked up and how much impedance is there), and voltage measurement independent of the power wires.
I imagine your non-canbus chargers did that primarily because of not communicating and knowing the balance. The difference in voltage between 95% and 100% is so slight that a charger has to be very careful if even one cell was out of balance. The BMS and DC/DC converter put a small load on the battery and perhaps higher when it starts to balance which may add to this complexity?
I'm no expert either, just hopefully adding to the discussion and understanding.