AFAIK not exactly, under 64bit mode you can run 16bit protected mode but not 16bit real mode code. While this would be an issue for Win1.x/Win2/x compatibility, the majority of 16bit Windows applications however are made for Win3.x which tend to be made for 16bit protected mode.
This is basically why you can run 16bit Windows programs/games under Wine on 64bit Linux (though you may need to enable some flag via /proc or /sys i don't remember the name of).
Correct, AFAIK the main reason to not support Win16 protected mode was the size the relevant bits of HANDLEs which would have been severely limited to 16bits. Completely obviating the reason to use 64bit windows. As is HANDLEs are 32bits of significant data on at least through Windows 10. In theory now that Windows 11 has dropped 32bit support could be 64bits on Windows 11. All of this because someone will inevitably want to use the clipboard between a 64bit app and a 16bit app and it would have made things VERY painful. Could MS have written a layer that "fixed" that? Potentially but the number of people using 16bit software was relatively small AFAIK at that point.
But the page tables do technically support 16bit protected mode code when in compatibility mode under long mode AFAICT.
This is basically why you can run 16bit Windows programs/games under Wine on 64bit Linux (though you may need to enable some flag via /proc or /sys i don't remember the name of).