I think that the methods of charging EV`s may be evolving to some degree. I suspect for low mileage users using a 13amp socket may well work out well enough even though it will take longer to fully recharge the battery, perhaps looking upon that system as trickle charging, compared to other methods... Given modern battery`s chemical makeup is different and evolving, whether a slower charge is more beneficial to battery longevity or not.. I have no idea.
Using a 13 amp socket avoids all the many rules and regs relative to fitting an external wall connector to provide circa 30 amps.
Dependant on the electrical distribution network in your area it is possible that fitting a wall connector capable of supplying 30 amps may not be possible due to possible overloading the house supply
As best I understand it wall connector is not a charger, as it supplies standard household voltage to the EV which has an inbuilt charging system to modify the voltage and current to suit it`s and your requirements of the vehicle. .up to a maximum of circa 30 amps....
Charging a Tesla model 3 at circa 30 amps, takes an hour to put approximately 30 miles of range back into the battery.
The tesla wall connector is a smart device thus requires an internet connection to set it up, which in the past could create issues of range to connect to wi-fi...which could be worked around, but seemingly now simplified by the availability of a new cable to carry not only mains voltage but also a hard wired connection to your router.....
As ever given the rate of evolution in the EV marketplace that which I type above could be well out of date.
As ever more than happy to be corrected if anything I type may be incorrect..