So you build a machine that kills all tigers and now you don't have to worry about belief.

The problem with objective reality is 1. it changes. 2. it can be different for different people in different places.

If I live in rural India, there is probably not a tiger behind the bush. If I live in downtown Chicago there is almost certainly not a tiger behind the bush. This leads to the hard problem of probabilistic thinking which requires a lot more energy than black and white thinking.

Lastly, humans are real, and even incorrect belief systems create a reality you have to live in. God, for example, is almost certainly not real. Saying that in a forum will have some percentage of people downvote you and try to reply with a relatively poor argument. Saying it in the wrong place and time outside of the internet can most certainly get you killed. So just because something isn't real doesn't mean you should open your mouth at an inopportune time and learn the reality it created.