So do I need to sign up with every service concurrently, in case one comes out with a movie I like?
Basically, yes. Or you can wait until over time the movie you want becomes less valuable and additional services carry it. But this is all very complex and determined by contractual obligations in the original carrying service.
I use a collected subset of services based on certain criteria which are most important to me.
For example, I use Netflix as my primary base provider for most content. I do this because they have no commercials (my number 1 requirement), and they are reasonably priced, and they have a lot of their own provided content which I tend to like. So I get a lot of value from NetFlix.
I use Amazon Prime as my second source basically because it comes included in "Prime" which I already join for delivery savings and other perks, so it's essentially "free". On top of that they also have a lot of original content which I like, and they carry a good range of early run releases. They also own The Expanse, which is in my opinion, the best SciFi series to hit the airwaves in decades and perhaps ever. But never mind that.
Lastly, I use iTunes to purchase any individual films or series I would like to watch and own. This is mostly just a habit based choice because I began doing it over a decade ago when there was less choice. Today I could also choose to purchase individual items through Amazon or multiple other sources.
I specifically do NOT purchase any services which include ads during any of their programming. For years Hulu did this and I refuse to use them because of it. I'm not sure if they have changed their ways, or if they just offer premium memberships to avoid ads, but I learned to dislike them from the ads early on and haven't looked back (mostly because my current arrangement with NetFlix, Amazon Prime and iTunes covers all my needs).
I also specifically do NOT use any service (like HBO or Starz) which just offer a stream of whatever they happen to be showing (originally on various channels, which is the old way of doling out content back in the cable days). The days of having to wait for someone else's schedule to watch the thing I want to watch are long gone for me. And just like with Hulu, if HBO and Starz have changed their offerings and allow you to select your content when you want to see it, I have not even bothered to look. For me, they were slow to the show and are now part of the trash heap of history.
Hope that helps.