For one, it ignores the fact that the child needs to eat when he needs to eat. He cannot always wait, and it sometimes will create a scene to force the issue. Yes, some can wait as they get older. I would expect my four-year-old to wait, for instance, but would not expect the same of an under-two-year-old.
So what about using a cover? I used a cover with Kieran until he was about 5ish months old, when I got tired of the hassle and he wouldn't tolerate being covered. I figured out that I could actually be more discreet by nursing without a cover, since I could feed more-or-less instantly and without an obvious indication that I was breastfeeding (the covers ensure no skin is revealed, but make it obvious what you're doing, in my opinion). I really don't know many children who like being covered to feed, to be honest. At least not when they're older than a few months' old.
Finally, is it really an act of charity to cover or move for the sake of the adults who may be uncomfortable? It would make them more comfortable, but is that the same as being an act of charity towards them? There are times when we need to be made to feel uncomfortable in order to truly confront something, and this can in fact be an act of charity. Charity doesn't mean we ignore our issues, or others' issues, but that we help them. In the case of breastfeeding, I personally don't think covering or moving is an act of charity for others, for it perpetuates the skewed perception of breasts as being strictly provocative and sexual instead of being the normal way mothers nourish and comfort their children. Again, this doesn't mean purposefully drawing attention to oneself or being belligerent about it, but simply feeding one's child when and as needed.
It should also be noted that not using a cover or moving doesn't mean exposing oneself, either. Nursing without a cover can be done modestly. I've stood face-to-face with a priest whilst breastfeeding my daughter, and the priest only commented that she was sleeping, so I don't think it was obvious that she was also breastfeeding. Or maybe he just didn't care. I personally have no problem with wearing something that can be easily pulled down at the neck, but another way of doing it is to wear a camisole under a shirt and pull the top shirt up. While I prefer the former, simply due to ease, I could compromise and do the latter. Another option is to feed the child in a carrier like a mei tai or wrap, though this is easiest if the child is already in the carrier and is a bit smaller. I can still do that with Charlotte, but it isn't as easy as it once was, and since I don't usually wear her on my front, it would probably require more time and distraction.
In the end, I just honestly can't see covering or moving to be a true act of charity, for the mother, the child, or the other people. I know I'm a lactivist, and thus my views will be biased in that direction, though I've tried to think and talk this out with an open mind. I just wish it weren't an issue at all, especially not in a house of worship. Our Lady of La Leche, pray for us.