No, there's no way to do it! Personally, it's the most annoying thing about ANY Apple product, and makes me think that the top brass at Apple are either 1) so rich they have a butler wake them up each morning 2) they don't have an iPhone or 3) they sleep with their heads up their own ....
Seriously, is there one good reason why they would make it impossible to set the volume of the alarm??
They've reputedly just sold 500 million iPhones, and what percent would like to use the phone as a morning alarm? There's got to be at least 1 million people each and every week that get ****** off with this, so why wouldn't they change things ... It's insane, stupid or pathetic - take your pick