My own (slightly limited) experience and reading of the EV forums would suggest otherwise (at least for the LEAF), or that that info is outdated.
a few tidbits:
--lots of folks just use the L1 charger exclusively without a problem. Depends on your needs.
--I think the charge is roughly 'constant current' for L1 and L2 chargers. My Efergy home energy monitor shows the leaf is pulling 6.6 kW, its rated draw, up to the end, where the car reports a 86 mile range, and 12 out of 12 bars, or 100% SOC.
--L3 chargers are programmed to quit at 80% SOC to avoid overcharge damage to the battery. They are still supposedly 'hard on' the battery, not for everyday use.
--Until recently (2013 MY), EVSEs were $2k, and all chargers were 3.3 kW. With a 3.3 kW charger (or an undersized L2 EVSE) you would see a less dramatic improvement (3.3kW/1.3kW = 2.5x faster). Would you pay $2k for a 2.5X speed up or would you gripe?
--I paid $650 for a 5X speed increase. For me, this allows (i) two 'max range' drives in a day (with a 4 hour home charge in the middle) rather than one, or (ii) if I deplete the car and come home at 11PM, I have a fully charged car in the morning rather than a less than half charged one (at L1 rates).
--Even after the car is fully charged, it continues to 'blink' the EVSE so it looks like it is still charging for another hour or more, but the efergy shows very low draw. According to EV forums, the Leaf is trickle charging the accessory battery during this time...
--Yes, the Leaf has a regular car battery in addition to the Li 'traction battery'. I suppose you can listen to the radio and charge your phone while you are waiting for roadside assistance after bottoming out your traction battery.
Joking aside, when your phone runs out of juice it crashes or goes dead. When the traction battery is 'done', the car's systems are still 'live', so the little voice can tell you that you are out of charge, and display a 'turtle' on the dash (no joke). Hopefully I will never see the 'turtle of doom'.