All models are wrong, some are useful.

Yes, there are theoretical issues with assuming PRNGs are truly random. However, there are also theoretical issues with assuming that Newton's law of universal gravitation is true.

I am confident is saying that more experiments have gone wrong due to not considering relativity, than have gone wrong due to the proper usage of a statistically sound (even if not cryptographically so) PRNG.

I also suspect that both classes of errors are dwarfed by improper usage or non sound PRNGs.