The kind of redundancy that Bob praises is something transit planners spend much of their time trying to get rid of, because on typical days when we don't need it as redundancy, we call it duplication and waste.
Transit agencies work on such tight budgets that it doesn't make sense to run, say, a bus line next to a rail line, doing the same thing, just for the redundancy. If the rail line is serving the market, the bus should be off somewhere else, providing unique mobility rather than duplicating the rail.
This is especially true in small cities like Bob's hometown of Ames, Iowa, or Great Falls, Montana. These networks' resources are stretched tightly to create the maximum amount of mobility for the budget.
Having said that, there are a few situations where an efficient network is also a redundant one.
Classic high-frequency grids provide redundancy for transit in the same way they do for cars. If one segment in a grid goes down, there's a parallel line 800m away that you can walk to in a pinch. It will probably allow you to complete the same L-shaped trip that you intended to make on the disabled line.
Ferries are more complicated. The long cross-city run of the CityCats mostly connects stations that are also connected by bus. The bus trip generally runs a shorter distance at a higher frequency, though it may require a connection. So there's no question that the intrinisic attraction of the ferry is part of what keeps it busy. There may also be secondary issues, like the legibility problems of much of the bus system in downtown Brisbane, where most connections occur. But there are also situations where CityCat and the smaller CityFerry does a link that's simply impossible by road, or much, much longer, and in these cases the ferry wins on pure mobility grounds.
Of course, bus operators generally have backup fleets in case they need to suddenly replace a non-redundant train or ferry line that goes down. In Australia, there are often standing agreements between government and private operators to shift buses into this role, and given a day's warning -- which Brisbane had -- it's not hard to replace a failed network segment with buses even while running the rest of the bus network.
So is redundacy a good thing in disasters? Of course it is. Is it a reason to design networks that are redundant all the time, at the expense of more mobility that could be provided at the same cost? No, probably not, because you're weighing a rare disaster against daily inefficiency. Are there styles of network design that are both efficient and redundant? Yes, the high-frequency grid comes to mind.
In really big and dense cities, you can also get both redundancy and efficiency, because there will tend to be overlaps of service just to provide capacity into dense centers like Lower Manhattan, and in these cases, as Bob notes, redundancy is often possible. The key there, however, is that the duplication of services isn't justified by the need for redundancy, but rather for the sheer capacity need, and providing necessary capacity, of course, is part of efficiency.