There are 200 other countries in the world, and some come very close to the experiments you want to perform, now or in the past.
They let you look for correlations. They don't let you run a good experiment. People can come up with theories that explain the facts, just as MWI and the Copenhagen Interpretation explain the facts. Science won't save us here.
Sean Carroll, physicist and proponent of Everettian Quantum Mechanics, has just posted a new article going over some of the common objections to EQM and why they are false. Of particular interest to us as rationalists:
Very reminiscent of the quantum physics sequence here! I find that this distinction between number of entities and number of postulates is something that I need to remind people of all the time.
META: This is my first post; if I have done anything wrong, or could have done something better, please tell me!