I've got invisibility turned on also.
I hear what you're saying about the feature but I think it's a good one.
The fact people might get upset isn't our issue. They can take it up with all the people who have read but not replied if they wish.
Though do remember that often you find a lot of people read all the (latest) threads and then go back to the ones they have the time for at that moment in time, others they'll see if they progress or somebody with more experience replies first and go back to it if they remember perhaps.
I often (although perhaps causing more work for myself) open all new threads in a new tab - then read them one by one as I get time between doing proper work. A lot I don't get time to even reading and it'd mark it as I've read it still.
I'd then use the combination of "new posts" and "today's posts" to see which threads I have read and not replied to, to find the threads I want to reply to that I hadn't done so already.
Swings and roundabouts a lot of people use the forum differently - And I don't think it's a bad feature to be honest. It might even encourage people to reply if they have read a thread and wouldn't have done so otherwise - and content is king after all.