I totally get the problem.
Even though the rectangle is a live shape, once used as clipping path, it looses the shape controls in Transform panel (and other places), and there is no way to set a Rectangle Width of the clipping group. So much for the integration...
I use a workaround and rotate the image first, using Smart Guides (or a plugin lately). Then the task collapses into the previous one. Rotating image back is doable with many ways.

Agree, this is time consuming.
A dedicated scaling tool seems to be a better solution indeed.

I have used that technique before and often it works but sometimes you only know the length of something thats on an angle. for example a Triangle or a Awning or something angular where you know the length but otherwise dont know the width or height

Adam, actually there is a method just like what you describe.
The only difference is that it has to be a rectangle (the height doesn’t matter, it just has to be a non-zero width or height).

You create a rectangle over your image, on top of the section you know the size of.
You select both the image and the rectangle.
You clip the image into it, by Ctrl+7 (or Object > Clipping Mask > Make).
You enter the new width you need for this (or height), and press Ctrl+Enter to temporarily constrain width and height (or not, if you have this lock enabled already).
You unclip it and delete the rectangle.
Now you image has the right dimensions for this section you had visible in the clipping rectangle.

That is draw a rectangle around your truck, clip, scale proportionally to 250 inches wide, unclip — no it is 250 inches wide :)
Simple as that.
Does it cover your request? If not — why? Please comment back.

+1 for being able to adjust proportions of image if you add multiple lines.. if would distort the image via width, height, angle, perspective. (as an option)

Often I need to place a photo of something and scale it to a certain size based on the content of the photo. For example. I place an photo of the side of a truck. And I know the truck is 250 inches wide. But the photo shows also the background.. and the image comes in at 10 inches. I want to be able to draw a line from one point on the image to another, and then I would select the line and the image and hit a button and a pop up dialog box would ask how long that line should be. And then it would scale the photo until that line matches the number Ii entered in inches or whatever unit was being used. This would also be great if used on an angle. It would really help to get things to scale quickly.

Meanwhile there is the Orient Transform tool from the AstuteGraphics commercial plugins pack that can do it.