Maybe even the "weaving" motion is from a slightly swaying cloth projection screen?
I'd be interested to see what the Lumiere train movie would look like if properly laser scanned in 4k with a wetgate.
And it's most probable that the previous kinds of processing were with bad tools or with some other deficiencies.
The proper path would indeed be somebody hi-res scanning frame by frame, all grain and scratches kept, each frame more than once with different lighting etc, and then starting from there and comparing the "restoration" results, always with the original(s).
Just as an example, a lot of techniques for removing grain remove the existing information. The different lighting scans allow a lot of advanced algorithms to restore what our eyes could discern from the real film but most of the processes remove etc.