It takes MORE time to patch a tire than to replace it with a new one. Your example assumes that you need to go out & buy a tube, but have the patch kit at home. It takes less time to just replace the tire if you assume the same conditions for both (either having both in stock, or having to buy both). Unless you get a lot of flats, the cost difference is almost too small to calculate. I've had one flat in the past two years (730 days approx). Since a new tube costs around $6 & a patch kit is $3, it works out to a daily cost of approx. 4/10 of one penny per day. There is a small chance that a patch will fail (if it's not applied correctly) while there is ALMOST zero chance that a tube will fail.

To answer the question, peace of mind is gained. It's a similar thought pattern to changing your own brakes. They aren't that hard to do, but for many people it's worth the additional cost to make sure that they will not fail when needed.

Donating them to a co-op is not a bad idea. If I start to get more flats, I'll save them & when I get a few, I'll swing by & drop them off.