Yah, memtest is great for ferreting out specific memory errors, kinda thing I use when I know there's a problem then go hunting for the problem. That floppy issue is a DMA thing I think, though if you're running off hard drives or substitutes you may notice sound issues first with DMA failing to work correctly for the digitized sound.
If you have a perfectly behaved system, and change one thing, like you've had slackarse memory timings on 80ns SIMM and get some shiny new 60ns to put in, then it is most efficient to go straight to something like memtest that is highly specific to the changed component to get it tuned to perfection and get it running right. Likewise if you have a perfectly behaved system running great for months, then a problem occurs, it is appropriate to use tools to delve into that subsystem individually, start at the leaf and work down the branch. Most efficient use of time.
However, should you have just assembled a system or done many part swaps at the same time, you want a highly general test to see how it's all working, preferably one that works the core of the system, so that you know the trunk of your tree is sound, before you go worrying about what symptoms various leaves and twigs are showing. Unless you do this, you might be swapping floppy drives and controllers, going through a whole pile of soundcards, because of the DMA problems and never realise you've got garbage generated in the core of the system flaking everything out, and not multiple issues with random peripherals.
So you can say things like "If a floppy doesn't read the disk is bad, if three floppies don't read the drive is bad" etc and these may be true in certain cases on a system otherwise known to be stable, specific diagnoses of problems. But you sound like a complete clown if you start from this end before you have established the "otherwise known to be stable" part.
Unicorn herding operations are proceeding, but all the totes of hens teeth and barrels of rocking horse poop give them plenty of hiding spots.