Just to add to this - floating rate loans are common here, with a fixed date of mortgage ending. So an early payment in this situation leads to a lower payment next months (probably by a few cents or a dollar to 2 if you made a decent lump sum payment). It isn't much, but depending on initial mortgage setup a saving for next month can be realised.
To your point, yes, next month's payment has a higher ratio of p:i, but you have not "saved" anything...yet. In the end, the extra payments you make are just going towards reducing the maturity date of the loan. You are correct that the relative impact of making these extra payments early on does have a tremendous influence on the total interest saved over the life of the loan (and determines how many minimum payments you will chop off the end of your term). I didn't make that clear in my initial comment.