I wonder if self-reliance is really incompatible with most things, not just minimalism. At some level you rely on others, whether to farm your food or forge your steel or make your antibiotics.
Basically, what you are saying is that the idea of minimalism is incompatible with minimalism. Personally I think that there's some sort of conservation law at work here (or even entropy-like growth rather than conservation): the more you try to minimize one thing, the more expense you incur elsewhere - even if only at a psychological level (because, to confuse things even more, it looks like that at a psychological level minimalism is, in fact, a form of maximalism - similarly to, say, perfectionism being, in fact, a sign of feeling insecure and of distrust in one's ability to do a good job).