[freebeard]

I would have thought taking the inside line around corners to reduce distance driven would be better where it is not necessary to take a better line to get round the corner without braking.

This is just me opining, but.... What I'd called The Line and you call the inside track would take all the width available between dotted lines and other cars and give the minimum lateral acceleration.

Why might worn tires be desirable?

In a word -- hysteresis. The tread blocks squirm through an S-curve through the contact patch and that produces heat, which comes from fuel.

edit: If the tires are too new, they might be shaved perfectly circular as mounted on that rim at that time.