Zipdisks were overtaken by CD-R tech, which started out expensive ($2000+ writers, but with $100 readers in most machines) but quickly became too cheap for zip to compete (almost every CD-ROM drive was also a writer by the time DVD took over.)
Actually, I would expect the more likely killer to be USB thumb drives. No need to invest money or space in a drive at all, so they were usable even on your friend's or your university's or your employer's computers. The disc-based systems were woefully fragmented with a lot of confusion over R version RW and + versus - and CD versus DVD. It was more convenient to rewrite data than CDRW (how often do you need to permanently store data? Rewriting is the better use case). And the media was small enough that you thought nothing of taking it everywhere with you (like your keys and wallet). Plus, I would wager that USB thumb drives are more reliable than CDs, given the propensity for cheap CDs to delaminate or get scratched up versus the numerous thumb drives sent through the washing machine in pants pockets and still came out working.
