I agree, I have no issue with it being legal, but I have very largely heard that it was not. Well, changing physics kinda bothers me, so...
This is actually a question I have the background to tackle, so I'll give it a shot.
Basically, the more information you have to reveal before your opponent has to make their "move" the more of a disadvantage you find yourself at. This is because showing your hand early is bad, as your opponent may have eliminated a stage you would have struck yourself
With our current 5-stage system, the distribution of moves looks like this:
Player 1: first and fourth moves (Worst Move, Best Move)
Player 2: second and third moves (2nd Worst Move, 2nd Best Move)
As you can see, for both players, the 'strength' of their disadvantageous move is offset by the 'strength' of the advantageous move, so things even out. If you prefer to assign points to each move, 1-4 from worst to best, we see a balance:
Player 1: 1+4 = 5
Player 2: 2+3 = 5
Now here's why the "standard" 1-2-2-1 for 7 method is seen as unfair:
Player 1: first, fourth, fifth moves (Worst Move, Third Best Move, Second Best Move)
Player 2: second, third, sixth moves (Second Worst Move, Third Worst Move, Best Move)
Less symmetry this time, hard to match up moves like last time. Assigning points again we get
Player 1: 1+4+5 = 10
Player 2: 2+3+6 = 11
As we've been hearing, it's not balanced. Don't mistake the difference being "only one" as an indication that it's almost fair, player two is an entire move ahead of player one.
Now let's look at the proposed 2-3-1 method:
Player 1: first, second, sixth moves (Worst Move, Second Worst Move, Best Move)
Player 2: third, fourth, fifth moves (Third Worst Move, Third Best Move, Second Best Move)
Having to play the worst move is made up for by playing the best move, and the 3rd best and 3rd worst similarly cancel... But we see player 1 has to play the 2nd worst move while player 2 plays the 2nd best. Clearly unbalanced, but let's look at the points.
Player 1: 1+2+6 = 9
Player 2: 3+4+5 = 12
we see this proposed method is much less balanced than even the 1-2-2-1 method. Essentially, having to play BOTH the worst and the second worst moves is very weak.
Hopefully the math was clear and that answers your question. If you want me to work out the proof that it will always be balanced for 4n+1, feel free to ask.