Long lenses are typically used for portraits as the greater working distance they allow flatters the subject. This is due to the effect of foreshortening, the perspective is compressed when shooting further from the subject using a long focal length, making features like noses stick out less.
You can shoot portraits with a wide lens, but you're going to get funky looking shots that aren't always what you want:
You lose the sticky out nose effect by about 80mm or so (when framing tight). So why go longer? There's another plus when shooting with long lenses and that is subject separation. Longer lenses make it easier to get a nice blurry background.
My favourite portrait lens is the Canon 135mm f/2.0L, it's relatively small and light, and wide open it gives very nice backgrounds (better than the 85mm f/1.2 in my opinion):
Regarding aperture, blurring backgrounds is not just about having a really fast aperture like f/1.8 or f/1.4, in fact with some lenses like the Canon 24mm f/1.4L make it pretty hard to get a blurred background even wide open, without focusing very close. In the following shot I completely obliterated the background - at f/5.6!
How? By using an 800mm lens!
Finally, it's definitely not about looking pro - unless there were some advantage to a big lens pro's wouldn't use them and therefore it wouldn't look pro! Something like the 70-200 is a very versatile lens, long enough for flattering perspective, wide enough to use indoors and fast for low light. You don't need all those things at once for portraiture, but why buy an extra lens when the one you have will do great?
I don't worry too much about a large lens intimidating people - it's how you act as a photographer that will make them feel most at ease, not the size of the lens.