Yeah, I completely understand the desire for privacy. I think everyone should be careful with privacy. This app is really designed for people who want others to know about where they've been for a specific event like a holiday. Or perhaps you want to show someone all the McDonalds stores that you've been to, or all the locations of photos from work inspection sites around the city, or where a particular animal was spotted ... etc. So rather than sharing 60 photos with friends and then having to explain where they were all taken the map will automatically do that for you. There are different privacy options as well so if you only want some people to see your photos and locations you can have some control over that. There is also an option so that only the person entering the photos can see them (and only when they're logged in). You can even just use the app to view your photos on a map without even saving to the server so the photos never leave your computer (you won't be able to save the result but you can still view it in the browser without having privacy concerns).

Are there any good Wordpress plugins for putting up a gallery of geotagged pictures?

Not that I'm aware of. You can embed mapipedia pages into your own sites if you like. If you want any changes made to the embedded layout let me know.