With the goal of having sharable seeds, the smaller space could be considered beneficial. The right tool for the job is more important. Even an 8-bit LFSR is good for certain tasks, like randomizing particle effects for an NES game.
Here are the DIEHARDER results: https://www.johndcook.com/blog/2017/07/07/testing-the-pcg-ra...
As TapamN points out it is not cryptographically secure and can be broken. https://hal.inria.fr/hal-02700791/
But it's probably fine for non-crytographic uses (and indeed is widely used for such).
[parent comment has now added "non-crypto" to the original quote so that "all prng applications" is now moot]
http://taeb-nethack.blogspot.com/2009/03/predicting-and-cont...
Of course, nobody is in danger because your game's random state can be deduced.
But it can disrupt online play quite a bit. Just imagine what this can mean for tournaments.
Another good example of predicting RNG, after a large amount of gameplay, for a non-turn-based game:
https://www.youtube.com/watch?v=1hs451PfFzQ
I think in certain Pokemon games, people figured out how to predict and manipulate random encounters based on an animation in the load screen.