The discussion has switched from operating system to language. WRT operating system, DOS was never used on any of the 6502 machines. Apple developed its own. I believe Commodore did as well. Radio Shack could have used DOS since it was an 8088 processor, but mostly, maybe always, used the CP/M system instead.
I did not know that the BASIC language was licensed by Apple and Commodore from Microsoft. It must have been easier to port from 8080 assembly to 6502 assembly than to develop from Kemeny and Kurz' minicomputer original.
I cut my teeth on Applesoft BASIC, but I used only the integer subset; the floating point was too demanding, although now I don't recall why. Whether it ran too slowly, was too resource intensive, or-- probably-- was too hard to program and debug. I did some home accounting/budgeting, but did it all in pennies rather than dollars, and avoided division operations.
Since the Apple ][+ was the native computer of the original VisiCalc, its 6502 base code and its proprietary DOS were responsible for moving the PC from hobby toy to business computer. For an accounting firm to be able to do some of its spreadsheets in house is what triggered business' interest in PCs. This was a couple of years before the IBM PC even existed.
You are right on the timeline of IMBM-DOS, and I was misremembering. IBM PCs first arrived around 1982 as I recall, with IBM originally planning a single one time production run of 250,000 that would, they thought, completely flood the hobbyist market. Then Visicalc came along, then Lotus 1-2-3 for the IBM, and then IBM foolishly lost control of the market they had created by getting caught up in internal power struggles, while all the IBM clones came along. I believe the Compaq came out in 1984, along with a bunch of lesser machines. They went with MS-DOS as IBM would not sell its DOS to hardware competitors. However I was working with MS-DOS v3.1 as the newest and best in 1987 on a Novell network, and in my recollection v3.0 had come out only a year before that. But again, I might be misremembering. 'Twas a long time ago, in CPU years.