Because the difference between a rocket and an ICBM is basically non existent and being able to simulate the environment inside a rocket engine would help a lot with designing either. To do pretty much any job in aerospace you'll have to qualify under ITAR which means you'll have to be a U.S. citizen, lawful permanent resident of the U.S., protected individual as defined by 8 U.S.C. 1324b(a)(3), or eligible to obtain the required authorizations from the U.S. Department of State.

So, why don't we have these restrictions in Canada, Japan or Europe? Many countries have advanced aerospace programs. The only reason that I can see for those export regulations to exist, is because eliminating them would require effort and PR risk on the part of politicians.

ITAR is a little old so it's a bit crufty from a different time. But also I'd be shocked if ESA, JAXA, and CSA were completely open.

True, however there are other countries that are considered allies of US at the extent that new technology is ok to be worked on (more specifically HPC).

https://fas.org/sgp/crs/natsec/RL31175.pdf