>He still spends quite a bit of time finding keys on the keyboard, so that'd be a major distraction and would break flow.
I don't have kids yet but I am wondering if perhaps letting your child use a keyboard that is without printed letters could help them learn to type better.
Back in 2010 me and a good friend of mine decided to buy a TypeMatrix 2030 USB keyboard each and to switch from QWERTY to Dvorak.
Now of course I am not suggesting you let your child learn Dvorak. Teaching them Dvorak would probably be doing them a disservice at such an early age because of the amount of QWERTY keyboards they are likely to come in contact with.
But I think you should try to let your child use QWERTY with a keyboard that does not have any letters printed on it.
We bought black skins with printed letters and black skins without printed letters. In the beginning I was using the skin with the printed letters and I had to look at the keyboard for each and every letter I was typing. While my initial plan had been to first learn to touch type Dvorak on the TypeMatrix and then put on the skin without printed letters, I soon decided to put on the skin even though I had no idea where each letter was, in order to force myself to learn to touch type sooner. And it worked! It was really painful for the first two or three days. For each letter I was typing I started with the top left key and went through the keys one by one until I got to the correct key and then I used the backspace key to remove all of the letters I had typed which was not the one I was looking for. It was extremely annoying but it worked exactly as I had hoped it would.
Over time I've somewhat "unlearned" QWERTY, and for the first few years I was even carrying my TypeMatrix in my backpack pretty much at all times and in doing so I found it hard to use other keyboards even if I switched the computer to Dvorak.
After one of my keyboards broke due to wear from carrying it with me, I bought a new one but I stopped carrying it with me and started using whatever keyboard is available in Dvorak mode. I use the TypeMatrix at home and I have another one that I use at the office when I work but when I'm elsewhere I use for example the keyboard on my ThinkPad. Many keyboards will have QWERTY printed on them but since I am so proficient at touch typing Dvorak now I'm pretty much not looking at the keyboard at all anyway so it does no harm.
Anyway, point is, not being able to "cheat" by looking at the keyboard turned out to be a highly effective way to learn to touch type 100%.