Depending on the type of sign involved a photograph will not capture flat, accurate results due to the effects of perspective.
A photo is no big deal if you're just taking a reference photo of some flat panel sign whose graphics can be easily reproduced. If it's a more complicated repair job then a photo won't do much good. For instance if you have a channel letter sign with some complicated joined script and the trim-capped face is broken it will take one of two sources to make a new face. One source is the original art files. The other is making a pattern and then using that to manually cut a new face. A photograph of the damaged face won't yield anything that registers correctly with the rest of the sign. The replacement face won't fit properly.
Post processing a sign photo to remove effects of barrel distortion and perspective will work only so well. You can get really close by using a good DSLR mounted on a tripod (and using the right combo of lens and shooting distance). But nothing will yield a perfect fit thanks to the foreshortening effects of perspective.
It would be really cool if there was a kind of device that could draw/digitize large real world graphical objects and capture them into the digital realm without using a tablet surface. As far as I know nothing like that exists. I think a tablet-free pen would at least need to be connected to some home base device that accurately tracked the pen's location in 2D/3D space as well as record input data when one or more buttons are pressed.
Disagree. I've done this so many times with excellent results.
Perspective is no issue for flat images.
All you need is the size of the original sign.
Get a good DSLR / Mirrorless. a minimum of a 50mm lens.
Square up your shot - I.e direct centre of the sign, even if it's over head. Do your best to fill most of the frame.
Photoshop & lightroom have excellent tools to fix the geometry (you can draw lines on each size of the sign so the software knows exactly what to square up.)
Crop the image to suite the sign and save.
Open a new artboard with the exact size of the sign.
load up the photo of the sign
resize to fit the artboard.
Do this properly and it'll be near perfect.