Welcome to TM too, Pete..
Yes, the glass encased wires are supposedly a generation on from the times when you had to be careful cleaning the inside of your heated rear screen. In those days, you had to have a light touch so as not to break the very fine red lines that went across the glass.
Fast forward several years and the heating elements are now even finer, but run top to bottom of the screen in zig zag patterns.
Ford offer them in their range of cars, and they suffer almost as much as the flat screens Morgan use. It's usually just one vertical line that give up but, like the flu, it spreads and breaks out at other places on the screen
I'm led to believe it's down to the massive temperature ranges the glass is subjected to that stretches and tensions the elements, but how accurate that is I have no idea.
If the whole thing has packed up, it's probably a power supply issue and you can start tracing the two feeder wires to check for voltage, but if it's single wires or multiples only, then power is getting in there but missing those parts probably due to breakage.
The elements should be encased a lot deeper than they always used to be, so cleaning the screen ought to be an easier & less stressful process but I'm a coward and always use a light touch with a clean cloth and screen cleaner, and never a dry cloth.
I don't think there's an easy answer to screen demisting. Blowing hot air on works, but is clumsy and takes a hot engine to be effective. Air conditioning is the best answer as it takes the moisture out of the air, but that's a 'busy' solution.
My screen mists up with the roof down or up, until it warms sufficiently to stop the water vapour condensing on a November morning. Just add in a low sun on a wet road for the perfect morning drive...not...!!
Good luck, anyway.