Apparently it's possible to replace the default 16-color VGA driver on Win9x, using this guide from MSFN.

The guide used a patched Win3.x SVGA driver, and was meant for Safe Mode (SYSTEM.CB), but the same could be added into Normal Mode's SYSTEM.INI as well, and I've confirmed it working. With its settings I can get a working 1024x768 256-color base desktop, and this fixed a critical issue for my system, that when using the default 16-color VGA driver, opening any windowed DOS prompt will freeze the system which leads to a BSOD pointing towards V86MMGR. The cause of the critical issue is still yet to be known, maybe it's due to my graphics hardware and monitor combination.

It's not without issues however. I'm running WinME and after installing whatever necessary updates on the system, I noticed the mouse cursor stopped being rendered properly. Not sure which update caused the issue. Additionally, there remains a question that I'm yet to find an answer: What is the so-called 386 grabber (3GR)? The Win3.x SVGA driver uses "vgadib.3gr" instead of Win9x's "vgafull.3gr". I haven't experimented whether it'll work with "vgafull.3gr" or not, so this question remains open for now.

By the way, I don't know if anyone has tried replacing the default driver with VBEMP 9x... as this driver is a bit more complex than Win3.x's SVGA driver. Not sure about its possibility... On the other hand, there's also a SVGA driver (Super VGA) on Win9x which reportedly worked on some very old video cards as far as I've tested (such as a Trident 9440), but doesn't really work on modern cards. Don't know if it's possible to patch it in a similar fashion to Win3.x's SVGA driver... will consider take a look at what exactly was patched in Win3.x's SVGA and see if similar traces can be found on Win9x ones...

EDIT: Forget about diffing... the original and patched ones are too different...