it is literally impossible to have a small budget for a modern CGI-heavy action or animated movie
That depends on what you're trying to make. Disney's Beauty and the Beast has excellent animation, was well written and performed, got nominated for a Best Picture (which was such a shock that animated movies soon got pushed into their own category, away from the serious live action films), and was produced for what would be in today's dollars, a $41 million budget. A few years ago, Disney released Tangled, which has excellent animation, was well written and performed, and did get some awards although not best animated feature, and was produced for what would be in today's dollars, a $273 million budget.
Both are good movies. But Tangled, which cost over six and a half times as much as Beauty and the Beast, after adjusting for inflation, is not six and a half times better. You can make perfectly good movies on lower budgets.
The special effects for something like Avatar, Star Trek, The Avengers, etc, for $100M+ alone.
And yet, everyone loved Star Trek when it was on TV, and had such a low budget that they had to use the backlot for the Nazi, Gangster, and Roman planets, and the villain of the week was the giant floating head of Zsa Zsa Gabor! And everyone still loves The Wrath of Khan the most, and adjusted for inflation, it was made on a $26 million budget.
You know what would've been a better use of my time instead of seeking ST:ID? Seeing Trek in the Park.
Arguing that "if someone spent too much creating their content that's their problem, everyone should still be able to consume it for free" or "expensive movies are sometimes worse than cheap ones, and I should be able to watch bad movies for free" make no sense either. If it's bad don't watch it. If you watch it you apparently thought it was worth watching so compensate the creators.
I'm not arguing the latter, but I am arguing something close to the former. If it were legal for people to make and distribute copies of works on a strictly non-commercial basis (no charge for copies, nor for the media, nor bandwidth, no tip jars, no ads, not used as a draw for something else, no donations -- all completely at a loss), then that would simply be a factor for producers to take account of in budgeting films. Just think about how happy Hollywood would be if going to the movies was mandatory, and that you'd commit a felony if you didn't buy a ticket once a week. If maximizing their income is our priority, why don't we force people to go? If not, then why should it bother us if their income is not maximized, or even if it is less than what it happens to be now? They might make less than they do now, but they'll cope, I'm sure.
And comparing copyright issues from today and 300 years ago doesn't make sense, as copying was limited by technology or skill
I have news for you: that's still true. The technology has gotten better, and some of the skills, like literacy, are more widespread, but pirates do not have magic wands.
Today 1000 people can put 2 years of work into a movie, and it can be copied in 10 minutes using cheaply available hardware.
And the movie studios are free to use whatever equipment best serves their interests for making their own copies. They are not at a technological disadvantage. A huge movie studio can afford the same gear that the average basement-dwelling nerd can. In fact, usually legitimate publishers have the upper hand, being able to act openly, serve larger audiences, and use better, faster equipment which is nevertheless has lower marginal costs. At most there might be parity, but pirates never have the upper hand unless publishers are doing something stupid to handicap themselves.
or legal threats (debatable as to whether it really works
I assure you, it doesn't work.
Think about Prohibition in the US, however. Telling people that alcohol was bad for you didn't get people to stop drinking. Telling them that it was immoral didn't work. Technological solutions, like denaturing alcohol so that it was poisonous didn't work. Legal solutions, like busting up the rum runners and speakeasies didn't work, and in fact resulted in massive corruption of the legal establishment instead! Ultimately, the issue was found not to be so massively important that continuing to cram Prohibition down the throats of Americans was worthwhile, and the government basically gave up. There was some regulation of alcohol, and a few dry jurisdictions, but overall, the restrictions fell away.
Pretty much everyone infringes on copyrights all the time, and being unaware of it, or doing it completely accidentally is no excuse, due to the strictness of the law. It's widely felt that some amount of copyright is acceptable. But people break the law all the time, suggesting that we have more than the amount that people consider acceptable; their violations are only of the excessive portion of the law. If we reformed copyright, and shrank the law, it would likely diminish somewhat the profits of the copyright industry, but I think that's an okay trade for no longer making virtually all Americans criminals and scofflaws. If it means that movies with gigantic budgets stop getting made, that's fine. After all, no one misses the super-gigantic budget movies we don't make now, because copyright law isn't even worse than it is. All you need is good writing and good acting, which aren't too expensive, and the rest basically takes care of itself.