Maybe in the courts, but you can get your youtube channel shutdown or even be permanently kicked off your ISP (and the internet, unless you have more than one option) based on nothing but unsubstantiated accusations that you've violated copyright
It can, depending on the nature of the content and how creators distribute it.
Anyone can find themselves forced to defend their innocence after being hit with DMCA notices, but content creators are especially vulnerable because they depend on their works being publicly available. They have a lot more at stake (including the ability to eat and pay rent) if they are hit with accusations.
They are the ones who'll be hit by poorly implemented algorithms (like Google's notoriously terrible content ID or the many even worse imitations created by companies without the talent/money/data google has at their disposal) or can be targeted specifically because their creative works are perceived as a threat to some company.
The DMCA is often abused to silence criticism, to hide unpleasant information about a company or individual from the public, or to attack competitors. It costs very little to fire off accusations that have real-world consequences and as far as I know, no major company has ever been held accountable for doing so inappropriately, even when it's been brought to the attention of courts.
The standard in a US civil trial is preponderance of evidence, though, so all you have to do is convince the judge that it is more likely than not that the defendant copied the work.
Sure, but where the burden lies still matters. The plaintiff needing to prove copying is a lot more defendant-friendly than the defendant needing to disprove copying.