The reason for 1-1-1 diagonals is that variable movement cost increases the number of variables to keep track off:
- How many diagonals did I move?
- How many non-diagonals did I move?
- How many movement do I have left?
1.5 instead of 1-2-1 or 1-1-1 has the advantage of removing one set of variables, but it adds a further mathematical aspect - rational values. They are simple enough, one might think, we learn this in elemental school (Or is it later? So long ago...)
In D&D, this is further complicated by stuff like
- Hampered Movement due to terrain features
- Avoiding Attack of Opportunities
It's harder to predict how far you can go if variable movement cost are in place. Which means that sometimes, a distance seems to be coverable, but when tracking your steps to get there, you notice that variable movement cost and the attempt to avoid "obstacles" (potential AoO-takers) will mean you can't reach your intented destination. This in turn leads to people tracking their steps back, trying alternate paths, or changing their destination.
1.5 as cost for diagonal movement means that all the tracking/backtracking of movement means that you don't count, you compute. And that's slower or more error prone then just counting.
1-1-1 cost for diagonal movement at least eliminate one factor leading to this kind of error/backtracking. And thus it enables faster gameplay.
I am sure someone well tell me that they don't allow backtracking at your table, or it never happens. But I am not speaking about that someones special group, I am talking about general tendencies. And if we go by anecdotical evidence, I know that we have this kind of backtracking in each session where we pull out the combat grid, and I am sure no one would mind seeing less of it in my group.
Some may call it dumbing down, I would call it increasing usability.
