The data may live in the cloud, but it will be heavily cached locally. We'll still need several GB or TB of local storage, be it spinning disks, SSDs or permanent RAM.
Grandparents won't want to be without the home video of their grandchildren just because their WiFi router stopped working or their ISP is having problems. And it will be a long time before mobile coverage reaches everywhere you might take your computer: communications black spots, rural areas, Planes, Tunnels etc.