I drove 16,000 miles using this nearly universal plug connector on my vehicle:
If I lived in Europe, I'd be able to get over 3 kW from a similar plug. But here we're limited to about 1.5 kW in practical terms.
No matter, because most of us don't drive that far on a charge. Level 2 (with AC supplied at either 120 or 240 V single phase to the input of the car's onboard DC charger) is more than enough for most of us to use 90% of the time.
I plugged in at work- to a landscaping outlet- and again at night once the electricity time of use rates dropped. I charged at 240 V a handful of times in those 16,000 miles. It simply isn't necessary for commuting- it's only required for long trips.
Yes, a "quick charge" DC charger plug standard will evolve, eventually. But in an industry which can't agree on a standard for a 4 bolt wheel hub, or a headlight bulb, the likelihood that they'll voluntarily agree on a single standard plug which must work with vehicles with battery voltages ranging from 200 to 800V, with charging rate capacities via direct DC ranging from 15 to 150 kW (and higher still in future) is very doubtful. It would require cost and compromise.
And yes, this is a major problem for the industry.
There's a standard for the "level 2" AC connection to onboard chargers, limited to about 6.6 kW- it's the SAE J1772 connector that every EV on the market can connect to, either directly or via an adapter provided by the OEM with the car. It's the connector that all the simple level 2 EVSEs ("charge ports") use. The charger itself- the AC/DC conversion and current control circuitry- is onboard the car itself. The EVSE is just a mute plug with a ground fault interruptor and contactor, and overcurrent protection for the cable. There's a simple signal used to tell the EVSE when it's properly connected to a car, and when the car is "done" charging.
There were three "standards" for high rate direct DC charging: Tesla's own "supercharger" standard, ChaDeMo and CCS. I'm not sure how scaleable either ChaDeMo or CCS are to higher voltages and power levels. Tesla's own standard seems to be pretty well established and their supercharger network is a major selling feature for their cars.