it leaves me with more questions than answers
I'm finding that this feeling you're describing is exactly what they are after with this movie.
This search for answers is what we are all after in our lives out here in the real world, and we look to these different institutions to find answers describing how we should be: Hollywood, religion, communism, capitalism. We get excited about the ideas on offer from each of these institutions, expecting that they can bring on some new change or improvement in our condition. So, we dive in and commit to the ideas and, while it seems like something is changing, we can see only a faint relationship between what we are doing and the effect it is having. The effect is never what we intend, and it's never quite clear that, really, any of it is bringing about the great achievement we hoped for.
So, here we are looking at Hail, Caesar!
wondering what it's telling us, trying to find a prescription from it, as to how it's
should be, and what we find in the movie is a host of characters each on a search for the same kinds of answers, grappling with the same kinds of recommendations from the same kinds of institutions, getting excited about one idea or another, and on and on it goes, and has ever been throughout history.
This searching process is reflected in every aspect of the narrative in the movie, including the sense that, really, not much is actually changing.
For me, this is an astonishing accomplishment to have conveyed in under two hours' running time. The process of seeing this narrative, of finding it in the movie, is one of the great joys it offers. I'm still finding all kinds of loops and rhymes and jokes and associations even just thinking about it, three weeks later!