I never ride without at least one spare tube, and when I get a flat, I bring the flatted one home to patch it. Patching on the road is too problematic to fiddle with, and so I only do it when forced to because I've run out of spare tubes. This isn't too different than what you do if you use tubular tires, so there's nothing unusual with that approach. I don't worry too much about what I would do if I were riding through the deepest jungles of Africa or the steppes of outer Mongolia, since I very much doubt I will ever ride my bike there.

There's nothing wrong with Schraeder valves if you ride on low pressure tires, but even then, once you know how to use it, a presta valve is much better. I only used Schraeders for years until I finally could afford a better bike.