They copied this driver model from UNIX/XENIX. However the way it was implemented in DOS, the interrupt routine had to always return with the "done" flag set, so a driver that was compatible with it wouldn't ever be possible to run asynchronously on a newer version.
There actually was a multitasking version of MS-DOS, but it was only licensed to a few OEM's. These disk images surfaced about 10 years ago: