I agree that Skype is becoming more and more a pain to use but it's hard to leave Skype. Family members who are not tech savvy know Skype, it would be hard switching them to an alternative. Sometimes it's better to put up with something to get the reward.
The is the argument for being on Facebook, too. It's a compelling one, for sure. The value of being on a network is the value of the people on the network times the quality of the tool. Skype and Facebook both have such huge networks that they know they can let the tool quality fall dramatically without it hurting them too much. But Skype might be close to walking off the cliff at this point.
I faced this prompt too, when I launched Skype just 2 minutes before a critical phone call. The caller at the other end was kind enough to wait for the download to complete.