Those boots are hardly "unrepairable"... Just an expensive rebuild, probably close to $100. In the 20 years I owned and operated a shoe shop we often saw worse. Much of the problem here is that the original parts are missing and I assume discarded so it is hard to be sure of exactly what they looked like and sizing is a little harder without them. They tell the story of the thickness of the sole and things like heel height/shape. I don't see any markings from a wood, fiberglass or steel shank which also indicates a unit sole was likely. It appears that the original was a unit sole or at least a cemented welt process. Some of those molded unit soles can be hard to acquire in the needed sizes. There are usually other options though.
Heel seats "can" be replaced and normally a leather counter can be sewn in as well to get away from the sagging there.
If someone built something to start with it can usually be rebuilt. Note though that it is sometimes impossible to rebuild "exactly" like it was originally especially if the unit sole was injection molded directly onto the upper.
Any "good" shoe repair shop can do this job but you might not want to pay for it.
I'll probably make somebody mad here but just because someone has done something for a living for 30 years that does not always mean that they are worth a rats behind at it. I have known a lot of tradesmen over the years that were barely "adequate" at their job but survived by turning down all of the difficult stuff to avoid looking bad. At least the smarter ones know their limitations and take on work accordingly.
After I retired from my shop (and sold most of my equipment to a highly skilled custom boot maker) my son took a pair of heavy work boots to a shop in a mall at a nearby town for new soles and heels. Fancy shiny place... Fortunately I had kept all of my handtools and was able to put them back together for him after they literally fell apart within a few weeks. They obviously had no understanding of what was required to hold them together. He considered taking them back but figured that since they had no clue the first time that a second try would be no better.
Good "old school" shoe repair shops are getting hard to locate.