Agree those conditions are rare and typically one needs to get things fixed anyways.

In some miles of touring, I've had three occasions that might match that description:
- January 1st, 1995; 12 miles from New Smyrna Beach, Florida. My right pedal shears off at the spindle. I ride with one foot to New Smyrna Beach and next morning I'm at the bike shop to buy new pedals (journal link: Atlantic Coast '95)
- November 2nd, 2002; 13 miles from Houston, Mississippi. My right pedal shears off at the spindle. I ride with one foot to Houston. No bike shop and it is Sunday afternoon. After some exploration, I buy an extra long spark plug, screw it into the right crank. I cycle the next two days down the Natchez Trace to Jackson where I buy new pedals (journal link: Natchez Trace, October 30th to November 4th, 2002)
- May 23rd, 2004; Paris Tennessee. My mistake in mis-threading my pedal in the dark after I arrived in Memphis results in the right pedal stripping out of the crank as I cycle through town. It is Sunday so I find a motel. The next morning, I go to the local auto dealership, rent a car and bring the bike to a bike shop to replace the crank and continue the tour (journal link: Memphis to Cincinnati)

In all three of those cases I did have toe clips and hence could ride short distances with one leg. However, one fairly quickly discovers that is extremely awkward particularly if you have no perch to place your other foot (hence the spark plug). Furthermore, it really is a problem that needs to get fixed, so one is mostly figuring out how to get to a spot where it gets fixed.

I've also had pedals seize up and go bad while on tour. However, the failure modes were more typical that I would get some warning, e.g. pedals sticking, so I had enough advance notice to get replacement pedals before it happened. Also on some more remote tours, I've also carried extra pedals. So even with experiencing some of these failures, I'm not sure that is a particularly important reason behind pedal selection. I agree it is more of a personal preference thing. I've been touring long enough that in my case, I still have cases of using toe straps and I also have a bike with double-sided pedals.