An educated guess could be made about which controller supported the original physical disks and synthetic images could be created using cpmtools against that format, but the resulting .DSK would not be a verbatim image of a disk that existed in the wild.
Such a synthetic disk image could also then presumably be marked BAD_DUMP as per your advice above.
With diskettes there definitely needs to be a 3rd marking to distinguish "bad" from "inaccurate" dumps, because areas outside the actual files often only matter for copy protected disks or bootblock position, so the indication should make it clear if the disk image does function or not.
With downloaded content or type-in listings from magazines the binary structure does not matter anyway, so there is no "master copy" to reproduce. Other diskettes often have bad blocks outside the actual files.
My main PC is a severely modded Highscreen Colani bigtower (DFI K6BV3+/66 mainboard with AMD K6-3+@550MHz, 768MB RAM, 2 genuine ISA soundcards, DVD writer, 160GB HDD, running Win98SE) which has a 1.44MB 3.5`` and 1.2MB 5.25`` diskette drive. Nowadays I have installed at its ceiling an additional modern ITX mainboard (Ryzen 2400G, 16GB RAM, 8TB HDD, DVD writer) for Linux Mint and Win10, so I first time have enough disk space to dump some 100 of my CDR (containing e.g. tons of downloaded ancient web pages about tech stuff etc.).
I am working through some hundred of my PC diskettes to preserve their contents. Some indeed were unreadable; particularly one brandless 1.44MB sort (black with white "HD" logo and too small paper sticker with cyan lines) tends to fail, and also 5.25`` things written with 360KB drives (ancient 286 and CPM machine at school) are partially unreadable. Often I have to carefully clean the surface with cotton swab and isopropanol (let it fully evaporate, else the surface is softened and gets scratched) and insert cleaning diskette with a drop of isopropanol between read attempts. Also rhythmically pressing the thumb on the front of the diskette can help to read bad blocks on warped disks. I had taken apart the external 3.5`` diskette drive of my IBM Thinkpad 760XD to rotate the head motor into different positions, which helped to recover a few more files.
(In former times my first PC was a 286 and later 386SX bridgeboard inside my very modified Amiga workstation (A500 in huge wooden case with handsoldered adapters, internal A570 CD drive, SCSI card for Iomega 20MB sort-of diskette drive etc.). At hat time I had often manually adjusted diskette heads because school diskette drives all seemed to be misaligned or dirty and so wrote incompatible diskettes, which e.g. made it hard to use downloaded files (through DOS ftp at school, had no internet at home). Thus many of my diskettes seem even worse misadjusted than original payware or shareware ones.)
For reading, I yet have only DOS mode of Win98SE for file copy (unlike windoze it allows infinite retries), a primitive track reading program disktool.exe and procopy.exe to mage binary images and check which blocks are unreadable. Bad with these tools is that they tend to replace unreadable tracks with random copies of previous tracks (likely garbage from a ring buffer), which makes them hard to identify in a hex editor (e.g. to merge multiple bad dumps).
I e.g. still have some unreadable 360K 5.25 CPM/86 disks from my practical course, those were likely written on a Siemens PG675(?) industrial computer (resembling an Osborne PC with internal green CRT), which was used to program Simatic PLC hardware. https://forums.bannister.org/ubbthreads.php?ubb=showflat&Number=106592https://forum.classic-computing.de/forum/index.php?thread/15021-siemens-pg675/https://en.wikipedia.org/wiki/Simatichttps://de.wikipedia.org/wiki/Simatic
The crazy thing is that there were some games on this computer. E.g. there was a textmode clone of "Qix", of "Centipede", of "Nibbler" and of "Ork Attack" (?, you had to move left & right to defend a castle by dropping stones on enemies those built ladders to climb up a brick wall); the latter even used a redefined charset but AFAIK none of them had sound. And I think I had copied them on my floppy.
My dump with disktool shows in HxD fragments of recognizeable words (e.g. file names) but likely nothing complete. At secondary school we also had on Commodore 286ers a CNC turning lathe and milling machine simulator (terrible DOS program that crashed with "division by zero" when moving the tool out of range), of which I still have diskettes with the code I wrote. But the disk with compiled code (for an actual Heidenhain milling machine?) is unreadable like when the disk wobbles eccentric and so only reads half of each track. But I guess it is the different head geometry that makes the Mitsumi 1.2MB drive of my Colani bigtower fail to read it.Reading strange 5.25 floppies?
Is there a program to read 360K (or lower?) DOS or CPM floppies in an Atari XL or Commodore C64 floppy drive, to convert it into a PC readable format? Eons ago I used a DOS serial port adapter (SIO2PC) to communicate with Atari 800XL and C64 to read and write their disks. Else I likely need a 360k PC drive. In a box of old parts I somewhere had a belt-driven double-height 5.25 drive full of DIL ICs (found in fleamarket scrap in 1990th) but I doubt that it works and have no clue what connector it uses and if it ever could be connected with PC hardware. It may have been gutted out of an Apple II or such.