Lets say I have an arc and I want to change the endpoints/handles/etc. but I want to preserve the length. Note that I do not mean the distance between the endpoints but the length of the curve. Is this possible in Illustrator? (It is probably super niche so I don’t know if this is something they would have thought of.)
This needs some serious programming that Adobe hasn't done. One possible excuse: Curve length is a math property which cannot be seen directly. Thus it isn't as important to visual designers as direct observables such as "are the lines parallel", "are the ends at the same point" or "is it straight"
Fortunately Illustrator shows the curve length in the subwindow "Objects" of the Document Info window. A competent programmer could in theory catch it and make the adjustment you wanted by iterating until the result is near enough.
Without programming nor add-on software one can solve the problem partially. It's possible to keep the start and endpoints of a curve and drag the size to one direction until the curve length in the info widow is good enough. I admit this seems clunky and artificial, but it works:
The black curve AB is too short (=about 100mm), we want 200mm without changing the endpoints and without making new twists nor nodes. For a start draw two help lines, one (=magenta) between A and B and the other (=green) horizontal from A
Select the curve, rotate with the rotation tool it around A until the endpoint meets the green line. It should snap if you have snap to point and smart guides ON
Reset the bounding box of the curve (=Object > Transform > Reset Bounding box). Drag it vertically longer until the length is near enough the wanted. With high zoom 200,000 mm is well possible.
Drag the start point back to A (=select with the normal selection tool, drag the start point with the direct selection tool, the curve follows if you do not click anything else)
Rotate the curve to its original position around point A