I've done some searching but I haven't found anything related.
I've seen that when tyres are worn out, the diameter of the tyre is smaller than when it's new. How I know that? The car lossses some top speed with the same gear ratios. Here's the prove. (just notice when the red point pops up)
Reply to what question ??
Since the friction on the tarmac removes matter on the tyre surface it makes sense to me that the tyre diameter gets smaller and smaller.
That's why your mechanic is measuring the depth of the tyre carvings to determine when the tyre has to be replaced.
I guess the opposite information (tyre diameter increasing when wearing) would have caused more reaction from the readers.