Yes but there will be hundreds of websites serving the same purpose that twitter does now. Most users will use a centralized page that they like. If the page starts putting up too many ads or god forbid censors someone they don't like, the user is free to host their own site or use someone else's.
That's the contradiction in your whole proposal. You can't both use a centralized (or multiple) website(s) and claim the project is decentralized. Also you can't not download the whole blockchain if you want decentralization.
You see this is a flaw in blockchain technology, it is not this magical tool that can solve every problem. It works fine for a payment system because of the incentive to run a full node outweighs the problems associated with downloading and verifying the whole chain but it won't work for anything else.