I hope the OP was not saying:
"Your e-bike will pull and shimmer if you remove your hands, so don't remove your hands".
Would not this be the same as in a car that pulls to one side because of an alignment issue? Seriously, if your bike does not track straight, or you cannot track straight and coast or peddle, without effort on the bars, then don't do it. Then again, you should be able to do both. That is basic bicycling skills. If it is the bike, that bike is a death trap waiting to spring. It is one thing on flat straight ground to have a bias (bike or body), but once you are at higher speeds, or cutting a curve or have to quickly maneuver and brake, or all of the above, any bias can be the difference between hitting the ground or not.
The fork rake plays a huge part in the handling geometry as does the rest of the geometry, so each bike will be different and a good dealer would put the person on the right bike. Old newbies are not suited for modern fast road bikes probably. Just my 2 cents.
Anyways, Thanks for the safety announcement, but I will continue to work on my handling skills, because it has saved me many more than once. And I am an extremely conservative rider. Likewise, I am teaching the wife those same skills and she really appreciates knowing what can happen and how to handle it when it inevitably does. Her confidence in riding has grown and so has her usage and enjoyment.