Fully discharging/recharging (more commonly known as a full cycle) myth come from the nickel-cadium battery. Since then we have the NiMH battery and now we have the lithium battery.
Ni-Cd battery have the memory effect, when recharging repeatedly not fully discharged cell resulted in a loss of capacity.
Ni-MH minimize this effect and li-ion virtualy don't have memory effect. I mean by that, fully discharging the battery and recharging it totally won't restore the lost capacity, in the case of Ni-Cd it restore the capacity, that's why so many people recommend to do it not knowing it's useless and in the case of li-ion, is not good as it prefer incomplete cycle to full cycle.
Quick charging is bad too, yes dash charging is so usefull when you need to charge it quickly but if you care about your battery life, don't use it every night.
Anyway whatever how you treat your phone battery, in 2-3 years the battery will lose most of his capacity