Actually, there is a good reason to pay your interest at certain times, but it won't apply to everyone. Interest is deductable on your income tax but there is an income phase out. It is likely that many docs post-residency will make too much to qualify for the deduction. Thus, if you have a spouse that works and a reason to itemize your taxes (such as owning a home), paying your interest may make since even if you loans are currently in deferral.
Ed