I left a job and offered two weeks. They said, no worries, today can be your last day. Translation, they didn't want to pay me for another two weeks, and felt that outweighed any contribution I might give over those two weeks.
Three weeks later a work friend of mine said he was leaving the same company and didn't give them any notice, and they were really upset about it. According to him they said, “You know, it's professional to give two weeks.” He still declined.
The point is, it's not about professionalism, it's all business and bottom line. If they think the business would financially benefit from paying you additional salary and having you around for additional time, that's what they go with and suddenly require.
If they think paying you additional salary will have no impactful benefit, then they go with that and let you go immediately.
Remember always that it ain't show friends and show family, it's show business. You owe them nothing, unless contractually obligated.