I would say it is unlikely - storage is so cheap that some form of local storage is likely to stay.

A terminal device still needs some form of storage to run the software to access the cloud. That might end up being some small storage on a chip but the difference is not between none and something, but some and more.

I also think there are enough people who want storage they own and control that it’ll persist as a concept. Also having devices that work when networks are down is a benefit in itself - attempts to make devices dumb terminals get exposed as a productivity nightmare when networks do go out.

I think big business will certainly try hard to lock people in to their ecosystems. Remote storage, remote computing/graphics processing are all ways they will try. But conversely there are vibrant communities pushing independent & private alternatives that I don’t see dying - whether thats Linux on PCs, or Graphene OS to take control of your android device etc.