Not everybody lives in large urban areas where Internet is an almost guarantee. I myself live in a remote area of Ontario where coverage can be spotty at times. It's nice to have a fallback to offline storage when I don't have access. Not everybody is willing to pay for a data plan as well.
Because:
1) subway trains have no wifi
2) concrete and refrigerators block signals
3) data is expensive
4) once I have all the data from the site, I want to read and play on it without necessarily updating every micromove with a ping and response
5) some services don't need real-time call-and-response. Would you want wikipedia live updating every paragraph when all you want to do is read an article?