The cost of debt goes beyond the dollars and cents you may spend on interest and fees. The true cost of debt is in the opportunity cost - the things and experiences you miss out on because you're too much in debt to enjoy them. Think grad school, vacation, early retirement.
Paying off your debt faster might let you get back to enjoying life - the way you did before debt crept in. Read What is Debt Really Costing You to get an idea of how much you could be losing because of debt.