We actually started with a local storage approach too during the first 1,5 year we worked on History Search. The reason why this approach failed is due to the size of the application—it to large have for mainstream devices. If you're interested I've written about our journey more here: https://medium.com/@martijnverbove/moments-before-success-or...

I like what Worldbrain is doing but their extension is a prototype. As you will notice they support plain-text search (similar to ctrl-f), and History Search is full-text search and won't impact your device's CPU load or memory.

On their website they mention their next version will be cloud-based too. This is not to spy on people but because of the performance demands of a full-text search engine and the applications—this types of services also require maintenance. Just to give an impression; our search engine alone is over 3,5 GB, this doesn't include the app or databases.

What I would recommend to try them both out and see which one is best for you.