I'm a bit late but wanted to post here as this thread was partially the reason we did it. My company (ISLOG) has such solution since 2005 (before NFC existed btw, known as a RFID logon solution) for corporate but this doesn't match end-user expectation and is a commercial solution.
But as this was requested several times on the Internet I took on my free time to create a free tool for this purpose, with my company approval. See ISLOG Logon NFC Community, it should basically match your expectation and work with what your call generic readers.
Otherwise you can take a look at compatible readers, those are the one supported by the open-source RFID / NFC library LibLogicalAccess.