Yes, like the squalling infant who decides just at the worst time that it wants to nurse, NOW!
Sometimes the women are just as put out about having to nurse in public, too...
Yes, in theory you can pre-pump milk and pack it...
but in order for it to keep it is better to freeze it; then you have to thaw it to just the right temperature, etc. etc.
Full Disclosure: my wife breast-fed. The kids didn't always care about the niceties when they wanted to tank up. ;-)
Well, my children ate on a pretty regular schedule, every 3 to 4 hours. Not too often are people forced to be away from a private place (with an infant) for that amount of time, hence my comment about refugees.
Either way, modesty is not about what YOU are comfortable with, it's about being respectful of those around you, who may not be as carefree with their anatomy and bodily functions.