“BIOS” is really just a bunch of drivers in ROM chips somewhere.
Thing is, most devices you actually don’t need special drivers because they are so standardized. Mice and keyboards are USB HID. There are a handful of ways you typically interact with storage, like using SCSI. Surprisingly, a lot of storage devices are actually SCSI, in some form or another.
One of the big problems is that drivers are going to closely interact with other operating system services, like memory allocators or the scheduler. The interface has gotten a lot more complicated over the years. And the semantics that operating systems present to the user are sometimes different in significant ways. Back in the BIOS days, what you could do through the BIOS was rapidly falling behind what you could do with a proper driver.
To pick on the filesystem example, there are some fairly major differences between Windows and Linux/macOS/BSD filesystems APIs from the developer perspective. Windows has mandatory locks and files are identified by name. On Linux/macOS/BSD, there's more of a separation between a file and its name—files do not even need to have names at all, and locks are advisory. For this and other reasons, there are some boundaries between files you use in WSL and files you use in Windows.
I’m just very skeptical here that you could introduce another layer between devices and the OS, that would be thinner and more direct than using a hypervisor, more flexible than just using a standard protocol (like USB HID) which your OS already supports, and work with multiple operating systems.