But I don't just use Chrome and I want to access my bookmarks not just on my own browser. I want access on all my browsers and in any setting where I wish to reach them.

If I was always using the same browser then Chrome would work, but there are times I'm working at a client site and don't have the ability to either use Chrome or sign in to my personal account, yet I wish to access a stored bookmark. This is where Delicious comes / came into the picture...

Maybe my use case is different?