While I agree that the iPad isn't a primary computing device for me, for you and many others, I think it's already being used as the primary computer by millions of people. I'll have to dig around to find some statistics, but the iPad easily replaces sitting down at a desktop or with a clunky Dell laptop (essentially a desktop). The iPad may not be the exclusive computer for a lot of people, but I think iPads and iPhones are the dominant computing devices for an ever-growing proportion of users. Personally I can't see getting away from a Macbook anytime soon, but I see the trends. iPads outsell Macs at roughly 2-1
Speaking of kids I read recently about the surprising popularity of the (supposedly dying) iPad Mini as their first tablet. I think these kids will be using the Mini and then an iPad Air/iPhone far more in the first decade and a half of their life than a laptop and by the time today's ten-year-olds are going to college the iPad could likely replace their laptop if they've been brought up on iOS. I look forward to iOS evolving to be more OSX-like, rather than vice versa, but we will see.
It looks like your question got cut off. "Let me ask you, what should a student...?" If you meant to ask what a student should use today I think it comes down to price and personal preference. I'm in my early 30s so I used laptops since the beginning of college and the iPad didn't come out until a few years after I finished grad school. If I were a freshman again I could imagine an iPad Pro with a smart keyboard and my iPhone being my main computers, alongside a wireless HD for extra storage.
You make a good point about fitting into a purse. I'm an above average sized male so 3 vs 4 lbs in a bag doesn't matter to me, but it will to smaller people. My 2013 13" Air is still going strong, but my next computer will probably be a 13" Pro (or 14" if they increase the screen size). I imagine the larger Macbook they have in the works will be very similar to the 12", albeit with an extra USB-C port.