Radius and reach are not the same thing.
The reach start from "all around" the attacker's square.
Radius is measured from a same point.
In the reach diagram, it makes perfectly sense that the attacker could hit the creature on the corner squares. It could at least affect 50% of the square in the corner, so it's enough to reach anyone there.
In the radius diagram, the 'logical' 10ft. radius circle is really a little wider than that.
If you put a 10ft. radius circle on the grid, like I did in the last diagram, the actual 10ft radius circle works well. IIRC there is a rule (of thumb?) in D&D that says "if the area of the effect covers less than 50% of the area of a square, a creature in the square is not affected". That's what happens with the Actual 10'R circle.
Oh, for the record, I think I'll stick with 1, 2, 1, 2, etc. We've gotten used to it in 3e, and it doesn't take much more time for us. The relatively small increase in simplicity probably won't be worth the added cognitive dissonance.
And even for new players, if you can keep track of how many times your character has failed the stabilization check after his hp goes into the negatives, you can keep track of how many diagonal squares you've moved in the current round.
I've never played DDM, so maybe I am completely equivocated (correct me if I am plz), but I wonder:
How DDM players can keep track of the HP, keep track of conditions (that last for a round and for the entire combat), keep track of who already acted that round, take into account difficult terrain, line of sight, reach, and all that about dozens of different miniatures and at the same time, say that calculating diagonal movement as 1-2-1-2 slows down the game?