No, it would take a long time to charge from empty to full. EV batteries are charged more carefully than phone or laptop batteries because you want them to last instead of dying every couple years (last I saw Tesla battery packs should last for 300k+ miles). There's a charging curve (different max charging rates depending on battery conditions) which allows faster charging when the battery is closer to empty and slower when it's getting close to full, so the 15-20 minutes is an estimate based on charging the battery from nearly empty to around 50-60%. You could charge up to 80-100% but you'll spend more total time charging even though you'll stop less often, which makes sense if you stop and eat or something, but if you're looking to make the best time, then you'll want to charge to 50% or slightly more if you need the range.
Here's a specific example of charging a Tesla Model 3 from 2% to 100%:
https://insideevs.com/news/506520/tesla-model-3-supercharger-test/
2% to 80% took 32 minutes then 80% to 100% took an additional 31 minutes (but 2% to 50% only took 16 minutes)
Note that this is for the long range Model 3, where 30% battery capacity is roughly 100 miles of range. An EV with a smaller battery would take slightly less time each charge but would need to stop more times to recharge.
It's like a phone, you can charge anytime you want. Remember that the "time at a pump" only applies to road trips since you'd normally charge the vehicle at night while you're sleeping like your phone or laptop. I'd much rather have to spend a few more minutes on a road trip than the time to go to the gas station every week or two.