The problem with that reasoning is that it still assumes past hashing somehow has an affect on the future. And that an average has anything to do with interval (there's a reason standard deviation exists, you might want to look it up before you keep throwing around the word "statistics" with any air of authority)
Do you believe that in any given second your odds of getting a share are better or worse than any other second? If not, why would it matter when you switch?
Now, someone answer me this time. If I'm throwing dice in a box and I get a point for every six I throw, does it matter if someone keeps swapping in different boxes? if not, how does this differ from hashing?
Let's try this another way then.
Based on the average submission time, you would submit 4x 128 shares in the same time it would take 1x 512 shares. Nobody can really doubt this; that's the entire concept behind the share difficulty.
Would you rather lose 1x 128 share or 1x 512? Because when the switch happens you lose whichever share you were on. I would MUCH rather lose the 128 (512/128 = 25% so it's only 25% the amount of losing 512). Utilizing this concept:
1024 shares have gone by. You got one of the 512's on time. Your loss was 512.
1024 shares have gone by. This time you were on 128's. Your last share was rejected. Your loss was 128.
I seriously can't fathom how anyone could possibly argue that this isn't true. And this is based on the long-term because that's what an average is. Every time we lose a share, we are losing the equivalent of up to 512 shares, as opposed to a maximum of 128.
The longer this goes on doesn't mean the less impact it has. On the contrary, it means the impact is GROWING. Now instead of 10x 128 shares (1,280) lost it's 10x 512 (5,120). Now instead of 100x 128 shares (12,800) it's 100x 512 (51,200). The number continues to go up with every passing minute.