Well, that's what you "suspect"...
I certainly don't think there'd be no innovation without copyright/patents. I suspect some industries are more dependent on copyright/patents than others, and I suspect that the movie industry is one that is fairly dependent on copyright. Musicians can tour, software can be iteratively improved by users around the world, industries like the fashion industry that have brand recognition and produce physical goods can support creativity by the sale of these goods, artists and authors might make an income from donations, and sometimes people just create for the sake of doing so.
I don't think any of these models would easily transfer to big-budget Hollywood style movies though. Theatre troupes may tour, but video post-production is not a performance art. Software can be iteratively improved by users around the world and become more useful, but movies need to be delivered by a consistent group to remain cohesive. People 'buy Gucci' or 'buy Prada', but they don't 'watch Universal Studios' or 'watch Paramount Pictures'--the brand value is not the same. Nor are people as likely to donate their money to a faceless movie studio as to an artist or author whose work they appreciate, and movie studios aren't likely to create just for the sake of doing so.
And you're right, the law doesn't currently effectively restrict non-commercial conveying, but it does currently effectively restrict commercial conveying (by movie theatres, video stores, and retail outlets), and this is where most of the money for movies comes from.
Yeah, I only suspect that there'd be fewer big-budget Hollywood style movies without copyright, I don't know this for sure, but I'd be surprised if it wasn't the case. And yeah, we might question the real value of big-budget Hollywood style movies, but apparently some people like them.
I think we should try to legalise the kinds of non-commercial activities that people have been doing anyway since non-commercial copying became possible. I think this is a matter of protecting personal liberties that are under threat. OTOH, I don't see a limited term copyright on commercial activities as so much of an issue.