great question.
I think it's not unlike that fact you hear that "we only use 10% of our brain." I always thought that was a bit odd, like saying that only 10% of the volume of a living room is taken up by furniture and people at any given point. Sure, but the space left over is important! Just because it's not obviously used doesn't mean it's not critical. Who wants to be in a living room without a lot of space to breathe and large windows and lots of light streaming in?
So multitasking seems to me somewhat like moving the furniture from your friend's house into your living room temporarily for storage while s/he has some painting done. For a little bit it's no big inconvenience to trip over another sofa or dresser because even though it looks a bit cluttered, there is no immediate issue (you can still fit into the room to sit on your sofa). If it persists for too long however you will likely start to feel less satisfied with sitting and reading in your living room, and this dissatisfaction may be pointed or vague. As a start, the whole experience will have less aesthetic value and probably be less conducive to creativity -- as we know creativity needs high ceilings, empty space and empty time of all sorts, and most importantly silence. (This isn't to say no music, etc but rather to say a certain singleminded focus on the task at hand.)
As long as you make room in your life for deep uninterrupted things, multitasking occasionally may just make life more interesting. Many of us, though, multitask by constantly doing things which are more than a little addictive, like checking email on cell phones or looking at websites while on the phone. The more these things become a habit the more, I think, one is likely to choose things to do which allow for e.g. email to be checked at the same time, and for the habit to be perpetuated. And thus less likely to choose to do whole genres of interesting things which require isolation, space, uninterrupted dreaming.
To Penelope Rose: Your advice was not intended for me but very applicable and very nicely shared. Thank you , James Lambert