The main arguments I've seen are speed and determinism.
However, a cryptographically secure, deterministic PRNG can be built from hash or block cipher primitives that have hardware acceleration, making them quite fast. Seed (and potentially periodically re-seed) it from a strong source of randomness, and you've got a fast and cryptographically secure non-deterministic PRNG.
I thought that "classic" PRNGs like the widespread Mersenne Twister even had issues that can cause practical problems when used in certain kinds of simulations (Monte Carlo, possibly) that rely on large amounts of random numbers, but I haven't been able to find a clear source for this.
I'm certainly defaulting to secure ones, and I'm surprised modern languages and libraries don't do this by default for their standard randomness functions.