This is an interesting thread. In the UK at ATC units we are specifically prohibited from using anything other than printed copies of reference docs unless the CAA approves otherwise. In my experience, those computer based systems that I've seen have not been particularly reliable and fail to deliver the goods at just the wrong time. And despite the fact that they should be easier to keep up to date, this, again, is often a weakness. So I guess I'm a bit hesitant about laptops on aircraft for this purpose.
Which docs are available on the laptops? If they're not critical to the flight, why carry them at all? If they are critical, a laptop seems to be a bit of a dodgy way of carrying them.
In the longer term, even if the laptop is not used for approach plates and the like today, no doubt as time goes by and greater experience is gained, someone will do it one day. I'd be interested to know whether that would be equally welcomed on the flight deck.