> How should a reader infer the bye order for a UCS-2 or UTF-16 file without a BOM?
Simple: switch to UTF-8 as the only encoding standard for sharing text data, keep UTF-32 as 'internal' runtime format for random access to codepoints, and get rid of all other legacy encodings (UCS-2, UTF-16, Extended ASCII with code pages, and all the other region specific encodings that popped up in the 70s and 80s because UTF-8 wasn't invented yet.
This general switch to UTF-8 should have happend in the mid-to-late 1990s (e.g. together with the web becoming popular), and Microsoft alone is to blame for dragging this shit along for the next three decades. If all Microsoft tools would only save text data as UTF-8 starting by the end of the last century, but still support reading all sorts of encodings for a decade or so, the transition would have been finished by 2010. Alas, that never happened.
And tbh, the file size argument for alphabets that don't fit into 7-bit ASCII doesn't really make sense anymore today where images and videos make up the vast majority of data volume.