To be clear, I remember those transitions being very smooth, but I was a Windows user. The first machine I bought without a floppy drive was my laptop in 2005 when CD-RW had long since replaced floppies on the Sneakernet.
My school was mostly iMac G3s and I vaguely recall the lack of a floppy drive being annoying once or twice, but the Windows machines had floppy drives and you could easily share files on the network, so it was never a big deal.
Heh - my school had AppleIIs and BBC Micros. My first year at Uni we used a VAX 11/780. I guess we had somewhat different experiences.
On the other hand, I think the most impressive and smoothest transitions I've ever seen in the entire personal computer space were Apple's transition from 68K to PowerPC processors, and almost as smooth their transition from PowerPC to X86. I'm still incredibly impressed with the attention to detail they showed getting those major changes to work so smoothly for users.
My school was mostly iMac G3s and I vaguely recall the lack of a floppy drive being annoying once or twice, but the Windows machines had floppy drives and you could easily share files on the network, so it was never a big deal.