> Can an electrician focus on his work when a young child is with him?
Yes, of course. This doesn't mean a 4 year old is coming along on a traditional 8 hour US electrician's shift. It doesn't mean the 10 year old is coming along to the dangerous industrial jobs. When kids get put into reasonable contexts they adapt, it's kind of what we excel at as a species.
However, I was absolutely learning how to do basic home wiring (at a semi-useful level for some tasks) and electrical theory before I was in my double digits in years. By the time I was 10 or 11 (hard to recall precisely) I was wiring up my own circuits (alarm on my door to not be caught reading at night) at home and doing dangerous things with line current. I certainly knew enough to be dangerous, but also did understand the basics of how AC and DC circuits worked.
To this day I can still do basic electrical work such as bending conduit, wiring in work boxes - essentially everything past the demarc. These were all skills I learned before I was a teenager by helping out on job sites.
> How can he teach the child the theory of electrophysics that is necessary to understand if one is to become an electrician? Do others at the site watch the children and explain the theory? Would you then not end up with teachers again?
How many working electricians understand things to such a deep level? While I certainly understand more these days than I did at age 12, I can't really say any of it would be useful on a typical residential job site. The safety aspect is pretty well handled by a few standard rules of thumb that don't require much deep theory-level knowledge.
I'm very much not anti-school, but anyone who thinks our current system remotely challenges most individuals seems to have an incredible lack of imagination to me. Yes, this requires far more effort from far more adults across the entire spectrum of society.
Edit: All I do know is that sequestering kids away from 'real life' is damaging, and I'm unsure anything can convince me otherwise at this point in my life. We can never go back in time and give someone those experiences later in life (brains stop making neural connections as quickly) so I do often ponder what is truly being lost forever.