Seems to me this was more a problem with Teslas build quality or design, because the Porsche Taycan and Audi e-tron GT have a two speed gearbox. From when I drove the e-tron GT this shifting was almost completely imperceptible, no lurching of any kind even when launching it in sport mode. If you're driving in anything other than sport mode the car will spend most of its time in second gear anyways, not even using it from a standstill.
The coolest part is the rear motor can be completely mechanically decoupled from the axel so it can just coast. Most other EV just shut of power to the motor, but Taycan can freewheel on the rear axle.
Jalopnik did a huge in depth on the whole powertrain that is really interesting.
https://jalopnik.com/an-extremely-detailed-look-at-the-porsc...
Actually, Tesla outsourced the transmission, first to Bosch then to Borg-Warner. Apparently neither of them could design and build a suitable gearbox.
Porsche has a lot of experience with gearboxes which probably explains why they can build a reliable one when dealing with the power and torque.
Note: power mode does not increase power, it just waits longer to turn off the ICE in order to improve throttle response
In single pedal mode, slowing down to a stop is a lifting the accelerator pedal completely and it will come to a stop in predictable manner. The brake pedal adds more regen and stronger application applies the brakes itself. From a stop, pushing down the accelerator starts moving the car. On hills, there is brake assist and works without any drama. Operating in reverse is the same way.
In dual pedal mode, or classic operations. While under motion, lifting the accelerator has a bit of regen until about 7kph and then creeps forward. To come to a complete stop, the brake pedal is necessary. From a stop, lifting the brake pedal starts the creep forward. This being an electric, even on inclines, the creep forward is consistent. Reverse is the same way.
At slow speeds, ie parking, it is easier to have the creep mode. Controlling speed with the brake pedal feels better. However, with experience, single pedal slow speed works well, just have to feather the throttle.
I've set the car to default to two pedal setup on start. I hit the single pedal mode switch every time I'm driving. It works well in a shared car setup. I do find it more weird to now drive with two pedals, but using the brakes still comes up even with single pedal driving, so if I do "forget" which mode I'm in, I'll still use the brakes when the car isn't slowing down enough.
Regarding the simulated legacy behavior, ie rolling back on the hill or changing torque. This is in the same line as simulating gearing in a CVT and simulating engine noise. I don't find it appealing and do hope car manufacturers have it as a configurable item, like Nissan has done with the one pedal driving. Here in a Japan, even the noise generator to warn pedestrians can be turned off.
The first is "Creep" which behaves like a classic automatic transmission. It basically matches the dual-pedal mode.
The second is "Stop", which matches the single-pedal mode you describe.
But there's a third mode, "Roll", which essentially mimics a manual transmission in neutral once speeds get below ~7 mph.
When I first got my Tesla, I came from a car with a manual transmission, so "Roll" made me feel at home and I used it for the first couple weeks. But once I tried out "Stop" mode and tried out single-pedal driving, I was sold. There's no going back. It's now exceptionally rare for me to use the brake pedal.
Tesla tried that in their original Roadster. It had a two-speed transmission. The lurch when the transmission shifted during launch was too hard on the transmission, and many of them broke under warranty. Tesla had to replace many transmissions. It was easier to fix the problem on the electric side than the gear side.
There's something to be said for a paddle shifter, but mostly for better control at low speed. For parking and off-road use, it can be helpful to map more pedal angle to a range of low speeds. This is more like the high/low range lever found on off-road vehicles and tractors than like a stick shift.
Mode switches are undesirable because they lead to "wrong mode" accidents. This is an ongoing problem with aircraft automation.
Behavior with zero accelerator and brake is an interesting question. Should the vehicle creep slowly forward? That's a classic feature, or bug, of automatic transmissions. Some automatic transmissions had anti-creep mechanisms to prevent this. If the vehicle comes to a full stop, should releasing the brake initiate creep? Should the vehicle roll back if on a hill? Some cars have "hill holders" to prevent that. For an electric car, those are all design decisions - the power train has no inherent behavior.