Is it practically okay to use darlington triple?
A darlington triple will drop about 2.1V across it at normal currents of up to 10A - I can see it being a bit higher at 80A, maybe around 3V - this means it will dissipate a power of 240W and this doesn't consider that the regulator is a linear type and there maybe as much as 5V constantly across the transistor (darlington or FET or single BJT).

This means a whopping great heatsink and a potential power dissipation of up to (and possibly exceeding) 400W.

May I recommend that you consider a switching battery charger using a big P channel mosfet - it might dissipate 50W in comparison.