This is very interesting food for thought. I've contemplated this myself as I am a huge packrat and have a very hard time getting rid of items for many of the reasons the article lays out. I've gotten better, especially after becoming Mustachian, but it is still hard. I especially pride myself on being able to have whatever I need on hand and be able to create something out of nothing so that I am never inconvenienced or in dire need of anything. I'm a master of substitution and can usually find something laying around to work for whatever purpose I need.
I've thought about this a decent bit and used to be of a similar mindset. But, the way my life went I had to move around the world... a lot. As a result, I learned the virtue in traveling (and living) light. One mental shift I've made is that most things that we need to do aren't critical right now. As in, I need to fix XYZ because I noticed it has some wear (or flat broke). The frugal mindset of fixing said item instead of purchasing a new one is a great start, but that often only applies if you have the supplies to fix it on hand. So what if you don't? Are you instead forced to purchase a replacement right away?
Often times not. Instead of looking at our lives as a cycle defined by a 24 hour clock, if we allowed ourselves to go to bed at night with unfinished projects then that ever growing to do list might not be that strange, nor stressful, when it's forced upon us. As a result, we could keep a log of projects that need to be done, and as those raw materials come available (that were in our past lives saved up for a rainy day) we commit them to fixing one of the logged projects. In other words, if we eliminate the self induced stress (or inconvenienced as you put it) by recognizing what ACTUALLY is critical, we can leisurely accomplish the non critical to do list with little stress or grief.
For critical items, such as the need for running water, sure. Have parts and tools on hand. For repairing that quilt because Fluffy got a bit uppity, scrap materials will come down the road eventually.