Sounds like a great opportunity for someone to create a new coffee shop chain specifically centered around the idea of seating people with laptops for a long time. Actually I'm not sure why this hasn't happened yet.
Because you won't make any money. If you have 20 * 2 seater tables you're looking at:
$60-80 coffee per 4 hours - x * $40 for four hours of a barista(s) - employee overhead - electricity - internet usage - business overhead - rent = < $0
Rent is the limiting factor in this model, you want to be in a high traffic area to get those customers but not have to pay ridiculous rent and still have a decently sized store. Not going to happen.
Internet cafes tend to be boring white boxes without food or drink, the walls lined with five year old crumbling windows PCs.
It seems like there is a middle ground which has not been explored, which is simply a more expensive coffee shop with more space, where you are allowed/expected to stay for long periods of time. I would pay for that.
You can call that an internet cafe if you want, but it wouldn't really be like any I've been to.
Interestingly enough, this is how some coffee shops operate in Tokyo. It costs $21 to rent a small private room with Internet access, computer and unlimited supply of coffee and soft drinks. According to article, these rooms are mainly used by unemployed people who can't afford to rent their own place.
