The idea of a fixer movement is interesting, but I'm not sure it makes sense. The reason most people don't attempt to fix things is that they have made a reasonable and correct assessment of the costs involved. If my coffeemaker breaks, I have two options: to buy a replacement, or to assemble the parts and the knowledge needed to fix it myself. Life is short, and even if the replacement parts can be procured easily and are somewhat less expensive that the item being fixed (not always the case), the time required to gain the knowledge to fix it makes the whole thing too costly. The availability of an inexpensive replacement is a bonus.
Mostly, though, the framework appears too general. It's not a question of fixing or replacing: I can fix something myself, or pay someone else to fix it, or replace it altogether. Each will be appropriate at different moments, depending on the thing broken and the frequency with which it might break.
The culture of fixing-by-oneself makes sense when replacements are prohibitively expensive, or there is value added by learning how to solve a problem that might arise with some frequency. Cars fall into the former category. I held off purchasing a new car for two or three years after I could have afforded to buy a new one because I had built up a reserve of knowledge about how the old one functioned: I knew which problems I could solve myself, which were minor, and about how much a repair might cost for those that were severe. Buying a new car has meant giving up all that knowledge. But, one tinkers there because fixing a car oneself is much (much) cheaper than having someone else fix it; replacement is not usually an option in these cases. The other end of the spectrum is the example Jacobs gives--replacing outlets in the house. It's worthwhile knowledge to have because it's a problem likely to come up repeatedly, and by picking up the knowledge, one can shift the work away from professionals and save both time and cost.
But there are also situations where replacements are prohibitively expensive but problems arise with such infrequency that it makes sense to have someone else fix it: Jacobs' garage door is one; HVAC problems seem like another (I have a few basic fixes that I know, which might solve low-level problems; if it's July and the air conditioner is out, I'm calling a professional). The person who comes to fix it is going to be (one hopes) a technician who has genuine knowledge of the situation, and has practiced it in a wide variety of contexts, or exactly the sort of person we ostensibly want to support (dignity of manual labor and all that). In these instances, the trade-off in saved time and knowledge makes opting out of fix-it-oneself the sensible move.