I agree with the sentiment, but in his linked project he says this:
Somewhat surprisingly, Trifecta does not touch the images it serves. This is a bit sad since it might be useful for the software to create thumbnails for example. The security record of most image libraries however is sufficiently depressing that it is not worth the cost to do any kind of conversion.
Apparently leaking EXIF data to the internet is not a concern of his.
Something you shouldn’t have to do in order to use the internet.
There are browser plugins that let you change your user-agent request header to masquerade as another browser (e.g., Chrome).