You can cherry-pick intervals where stamp prices outstripped inflation, and I can cherry-pick intervals where stamp prices stayed well below inflation.
A 12.8% increase (not sure how you came up with 15%) over a period where inflation was only around 7.8% (based on month-to-month consumer price index report) sounds pretty bad, but you seem to have missed the previous four years, where inflation was 10.1% and the price only went up 5.4%. For the interval between raising to 37¢ and raising to 44¢ (an 18.9% increase), inflation totaled 18.7%. If a difference of 0.2 points makes all that much difference, you probably shouldn't be using the first class rate anyway.