MS-DOS was structured the same as CP/M: there was a small-ish machine dependent part you ported (called an 'OEM Adaption Kit' at one time), and a hardware independent kernel. At least through 3.0 and probably later, it did not require a PC clone. It ran on all sorts of non-PC 8088/8086 machines. Ever run MS-DOS on an 80186 with 8" floppies? I have. Now, your apps might not run because of machine level assumptions (video, usually), but MS-DOS did.
But the real problem with almost-clones was (as you said) that in practice applications more often than not bypassed the "ABI" and went directly to the hardware, and admittedly that's not MS-DOS fault per se. The result was anyway that lots of software wouldn't run on almost-clones, especially if they moved around too many of the assumed interrupts (e.g. 80186-based PCs - they had some of the peripherals of the 8088/8086 integrated, just not exactly in an IBM PC layout). One system I ran across was an "enhanced" PC-like semi-clone, probably using an 8086 or something better - the local health services had just started a huge campaign where they tried to get everyone to volunteer for a health checkup, and they were followed up with a new one some years later, and on and on (it still goes on, to this day). Anyway, for that early start, they used this MS-DOS computer to collect and print information. But the printer didn't work - the PC was nonstandard. I went to the hospital and figured out why, and patched things and got it working (I don't recall anything today about what or how or even why I could).
CP/M applications though - they didn't, for the most part, bypass anything - maybe that's because people writing the software knew that the hardware could vary wildly. Screen-oriented apps like WordStar usually needed a machine-specific patch for that, but otherwise CP/M software was way more portable than MS-DOS software. PC software though - vendors just thought "IBM PC hardware" and that was it, for the most part.
There were many MSDOS but not 100% IBM PC compatible machines made that got hit in the market because of this, such as the Zenith Z-100/Z-120 , TI PC, etc. If the memory map and everything else didn't exactly match the IBM BIOS setup the application would fail.
Nostalgia is a helluva drug.
Were you using the Osborne-specific version or the "retail" version of WordStar, BTW?
The "Osborne-specific version" was the retail version...for the Osborne. Yeah, there was a 'generic' retail Wordstar...that you had to patch for your specific hardware if your combo wasn't supported out of the box. I had friends who's whole business back then was hacking popular CP/M apps to support less popular hardware.
There wasn't some compatibility nirvana. It was just easy to hack up a fix because apps were on the order of 10's or 100's of kilobytes, not hundreds of megabytes.
It had terminal capabilities (not to the level of termcap in Unix, but good) which meant that shrinkwrapped software like Wordstar would run on anything with an 8080, Z80, or NEC V20/V30 and CP/M. The Osborne 1's tiny screen was only 50 characters wide instead of 80, but software still ran on it.
It hit the sweet spot of abstraction for its time, and made it easy to write drivers for custom hardware that a new manufacturer might decide to make.