It was never as easy as writing to a floppy, but by 1998, when the iMac came out, it was pretty straightforward*, even though you needed burning software on MacOS 9 - but I think its always been drag & drop in OS X.
Anyway, there was never a single technology that took over from the floppy: email attchments took up much of the slack, then Zip drives for larger files, at least two sizes of Magneto/Optical drives, Syquest cartridges, optically-tracked super-floppies (which also read floppy discs), DAT tape backup drives and a doofus that let you back up your hard drive to VHS tape...
However, CDRs came closest to being the "new floppies" because ~$1 for a blank disc that could hold 600MB of data was an argument-stopper, even if they were a bit of a faff to write. Zip/Syquest/MO/Superfloppies - and even rewritable CDs just cost too much to stick one in the post without a twinge.
*Ah, but I remember the days (~1990) when you had to create your image on an expensive MagOpt disc or Syquest cartridge and send it away to be burned. to CD... then the days (~1993) when you could have your own burner, but you needed a dedicated 1 GB hard drive (1GB!!!) to build the image on - and not just any HD, but a special "A/V" one that could be relied on to deliver a sustained 150KB per second (150KBps!!!) during the burn or you'd create a "coaster*" (which was not a joke when the blanks cost $25 a go - now you'd be able to sell it as a HomePod stand!).
