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hippy
It doesn't, but then it is a simplistic model that can't take into account all permutations of people's circumstances.
It seems that you're already thinking along the lines of reducing total interest paid, and the way to do that is to overpay.
The reasons for not doing so would be 1) utility of liquid assets (you need cash now for some reason) or 2) you can earn better rates of interest elsewhere, that can offset the interest paid (including transfer costs), without any appreciable increase in risk.
2) is hens teeth.
[Edit] The alternative would be chucking it into your pension. The best comparison would be to a spreadsheet showing you the net present value of both.