I think that’s the normal reaction – it’s interesting but silly. It’s also the basis for the McGuffin in Snow Crash, and has some resonances (though probably not a shared lineage) with Marvin Minsky’s ideas about the mind.
IMO Dennett’s Consciousness Explained should be seen as the seminal book on this subject (see above for why I believe it is disingenuously painted as somehow controversial or incomplete). But it’s quite a leap from the way we commonly think about our own minds, and there’s a lot of sci-fi that can serve as a good warmup. PKD, for instance – just thinking about the premise of We Can Remember it For You Wholesale / Total Recall takes you pretty close to Dennett’s picture.