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While I understand the reasoning, it's not advised to drive with one hand on the stick áll the time. Only when actually shifting.
Even more so, it's not necessary all the time either. On a highway you have to shift to the highest gear, keep both hands on the wheel and both eyes on the road.

Where I'm from, driving stick is taught as a standard.
If drivers don't show to be sensible in the way that you simple "can't" do anything else with your hands but driving when driving, they shouldn't be in the first place. This goes for all ages.

Many moons ago, when I learned to drive, if you took your test on an automatic you had a restriction put on your license. And people who could only drive an automatic were scoffed at.

Where I live, driving stick is typical, and that's what I drive. Shifting gears is only demanding for so long; after a while, your brain gets trained enough that it's part of driving, just like everything else. While a nuisance when you need a free hand, there are solutions around, even while driving through busy city traffic (where you need to fiddle with the stick a lot more than on longer trips, as Barking_Bud correctly pointed out above).

Having said all of the above, I totally recommend a teenager's first car should be manual transmission. Having to switch gears manually really helps you get an intimate feeling for how things work inside the engine, when you can expect power and when you shouldn't, and generally how to take advantage of a car's engine.

Part of my driver's education was on a 1940 Ford 9N tractor. It had not only a clutch and a gear stick, but two brakes, a throttle, a choke and an uncomfortably high center of gravity. Driving it was tricky.

Er, take it from someone who lives in the UK (where stick shift is the norm) this would NOT do anything to stop teenagers being teenagers. Best one I saw here was an idiot rolling a cigarette while steering with his elbows! The real answer is to make teenagers drive little electric 2 person bumper cars until they are 28 (when their brains suddenly get into gear).

My kids want to learn to drive a stick shift. But our manual truck died, and a decent affordable used car with a stick shift is very hard to find these days. In all honesty, I'd rather have a 30-40 year old car anyway because you can repair them at home. Too bad those are considered "antique."

My last car was a stick shift. Blue tooth was a necessity. Only used it for receiving calls while driving.

I hope this push for manual does take off. In addition to reducing texting while driving, it might also introduce more people to how enjoyable it is to actually operate a vehicle, to enjoy driving rather than just seeing it as a way to get from Point A to Point B.