Here is what I wrote when I came up with the rules:
I've played a couple of games that involved my children. While they are fine at understanding the rules and how to apply them, they are clearly overwhelmed by the number of choices available to them and how well they would work in the current situation. With that in mind, for the next game I will simplify it a bit by leaving each character with just their at-will powers and a daily power. The utility powers seem to be the ones that add the most confusion. This puts the adventurers at a bit of a disadvantage, so to counter that we will only draw encounter cards when a black triangle tile is drawn. This might be pushing it a bit too much in their favor though, and I'm guessing that some characters will be more nerfed than others.
And the conclusion:
Tried it out. Everyone surprised me by picking a different character, which brought the dwarf fighter into play. Except he only has one at-will power and no daily powers. It was my son playing him, so I hastily chose a utility power that would be easy to use. Apart from that, we played as I described above. The game was much more relaxed since the team wasn't getting hosed by random things, but HPs were still being lost at a steady rate that people felt threatened. It also became clear that some of the at-will powers are pretty rubbish compared to others, so were never used. With all this new data in mind, rather than making a distinction between at-will powers and other cards, I will just give each player two cards - one which can be used as many times as they like and one which is limited. Maybe give them an extra card if they go to level 2 (my son rolled a natural 20 three times in a row in one game!). That way there is a definite choice to be made. I wrote a list of the cards to use next time and left it in the box.
Didn't need to use the Healing Surges at all, so maybe getting rid of them completely will keep some edge to the game rather than making it a walkthrough. As said above, kids don't actually care about there being a low chance of losing, so removing the edge isn't a big deal for them yet. When they get older we will introduce the real rules, but until then I am happy to play "bumper bowling" DnD with them since they enjoy it so much.
We've only played it a few times since then, and since we had played it the normal way a few times the kids really want to pick all their skills rather than use my pre-defined list. Which slows everything down again, makes it hard for them to have balanced characters, and destroys the point of simplifying it. It's probably been long enough that they have forgotten that part and I can sneak in the proper simplified rules again.