To expect cyclists to keep their hands on the handlebars?

Actually it's quite easy to cycle no hands in certain conditions. I used to do it a lot on a certain stretch of, admittedly, cycle-path rather than road. Never came a-cropper. Never tried texting while cycling though.

The balance depends on the bike as well as the rider. Some balance easier than others.

And drivers overtaking cyclists are always supposed to leave enough room for the cyclist to suddenly fall off sideways into the road, which often means driving on the otger side of the road while overtaking, just as it does when overtaking a car so your DH wasn't forced to do something he shouldn't have been doing anyway.

no hands on the handle bars

The common one round here is to bounce up the pavement at a red light and back on to the road the other side without a thought for who is on the pavement or what's behind them on the road.
I confess as a teen to riding my bike with no hands but obviously I wasn't using a mobile at the time and in our little town not much traffic.
That's my excuse anyway.

Was in London recently and a cyclist went through a red light at a rate of knots - there was no special cycle lane - and those of us trying to cross the road in a speedy fashion just had to get the hxll out of the way!!! And then they moan they get carved up. Surely it takes two and all that.

Cyclists can be irresponsible and that is deeply disturbing as it puts them at risk and the driver at risk of causing an injury through no fault of their own.

I have no problem with responsible cyclists like my SIL.

But round here they tend to ride in packs, which is hugely dangerous on country lanes.