What do you think about the simulation theory?

A million times faster running the same program - likely true. But no one runs the same thing. In your example, how much more complex is a five day model as opposed to a three-day model? Way, way more than twice as complex. And the newer model is more complete, I’m sure. I’ve been programming long enough to remember when we had to leave lots of stuff out in order for the code to terminate in some reasonable time.
Though you’re right in that individual CPUs are already bumping up against processing speed limits. The supercomputer mentioned contains many CPUs. Not all problems parallelize well, so great speed increases for array processing does not mean great speed increases for AI or speech recognition. Or simulation.

Access to porn. Navigation. Spellchecking. Didn’t struggle at all.

Eta: last one is half joke but “publishing your thoughts” can substitute for the pedantic.

Far more accurate. The three day forecast just a couple decades ago was a bit hit or miss. In generalities it was more or less right, but it really wasn’t something to be counted on.

Now, I can expect to know to the hour when it will start raining 3 days out.

I’m sure it is. That’s an example of how people just don’t run the same program in less time on a faster, more powerful machine, but modify the program to take advantage of the extra power even for the same application.
I’ve only read a bit about weather forecasting, but I’d suspect that a five-day forecast takes into account factors that can be ignored for a three-day one, such as relatively far away weather patterns.