Of course there is a point. The benefits of having location independence and "cloud" storage are the same whether the software is open source or not, or whether I share the information with others or not.
To give an example, I'm working on a story using Google Docs as my primary word processor. Yes, I could use LibreOffice - and if I had it as a local file that would be my preference - but Google Docs means I can edit it from my browser, leave the house, and then edit it more with my phone. If I'm waiting somewhere for a half hour, I can open my story and write a couple hundred words on my phone. If I get a great idea for a future story direction, I can make a note of it right in the document. If I want to read it to my son (he loves hearing the story I'm writing and reading it to him forces me to proof-read it), I can do this from anywhere as long as I have my phone with me. (I also use the commenting system in Google Docs to record where my son and I have read up to.)
If I had this as a local computer file, I wouldn't be able to add to my story as often and I wouldn't be as far into the story as I am now (32,000 words and counting). Yes, when it comes time to look into publishing it, I'll likely import it into LibreOffice for better formatting options, but Google Docs gives me an ease of use that locally installed programs don't.