This feature request was discussed with Campbell Barton during meeting 2021-02-23
Generated UV's from curves are always normalized in UV space (circumference and length are always 0-1). This results in UV stretching as the vertices of the curve are changed. I suggest adding an option to automatically adjust the generated UV's of the curve so that the UV's position in the X axis are adjusted per length of each span.
In some cases it's really handy to keep UV's completely normalized, so let's add this as an option and not a behaviour that cannot be turned off. I'm all for keeping it as a default behaviour though.
Here is a screengrab mockup that hopefully makes this suggestion easy to understand.
Suggested UI mockup in object data properties