Has anyone ever accomplished much of value in their two week period? It's rarely enough time to replace you, let alone give you any time to transition any worthwhile knowledge to them.
Usually it seems to mostly involve them groveling and offering more money, but I've never known anyone that said "you know what, that sounds great I'll just stay"
The last time I left a job I put in my two weeks notice thinking I would get treated like the other employees who had left which was a security guard coming and taking them to the exit while paying them for the two weeks. I expected the same treatment and had planned accordingly by starting my new job at the end of those two weeks so I could get a break (I was working 50-70 hours a week). This did not happen instead they freaked that my knowledge would be going with me and scheduled multiple training sessions so I could teach what I was doing and how I was doing my work. I worked those two weeks (no overtime at least) and they kept me right up until 3PM on my last day when they finally said I could leave. I had 8 training sessions those last two weeks and completed my work because I did respect my managers but I did complain toward the end that they tried to keep me until 5PM with nothing for me to do.
So yes some people do get some work done during those last two weeks. Saying that next time I leave I put in my 2 weeks notice and I'm taking 2 weeks vacation.