>Rarely am I the one to stand up for Google, but the DMCA is such a garbage law that they have no choice.

First of all, Youtube with their ContentID circus goes far beyond what the DMCA requires. The DMCA requires you take down content once you receive a proper notice with all the required elements. It does not mandate that you proactively scan all video and audio as ContentID does (but other jurisdictions may have such mandates).

And then, they have a choice. They can reject DMCA notices. This opens them up to potential liability when they do, if the other party decides to sue them and wins. Thus they probably will consider it a bad choice. It's so much easier and "safer" just to accept every bullshit notice for them. But it's a choice regardless.

Github recently rejected the DMCA notice from the RIAA (it took them a while but they got there eventually); at least I am not aware of any counter notice filed and mandatory wait period elapsing afterwards.

Try filing a DMCA against google.com and see if Alphabet takes down that page ;)
No, they will have their lawyers look at the notice and laugh it out of the room, instead of blindly accepting a notice like that.

>It's the video creator's job under the DMCA to prove themselves innocent, under penalty of perjury. (No such penalty exists for filing a false claim, BTW.)

No, it's actually not. The process is this:

1) Party A sends DMCA notice to Company

2) Company (such as Youtube) receives notice, checks if it conforms with the law[0], removes content and informs the affected party if it does, details what is missing to party A (if possible) otherwise.

3) Affected party B may file a counter-notice now if their content got taken down.

4) Company receives counter-notice, checks the formalities and informs the original party A it received one.

5) Original party A has now 10 business days to file a court action against the alleged infringing party. If it does so, it has to notify the company.

6) Company will restore access to the content after 10 business days (14 at most), unless the original party A files a court action and notifies company about this action.

If it goes to court, the original party will have to prove their copyright was indeed infringement, and if it can, then the other party can still mount a defense, such as a fair use defense.

If it's a nuisance DMCA notice without merit, and if the alleged infringer files a counter-notice, nothing has to be proven, the content will be reinstated (after up to 14 long days), unless the complaining party is actually willing and bold enough to waste their time and money, and the courts time, and files an action.

Of course, this is not how YouTube and their ContentID does it; they heavily disadvantage whoever has content taken down/de-monitized/"revenue shared", and they actually make judgments on counter-notices themselves (not just looking at formal requirements of such a notice).

[0] Or not. As somebody handling DMCA notices on a daily basis, I have seen many, clearly templated notices from medium and major companies which are very incomplete or outright inaccurate. One "DMCA as a service" company likes to file notices for user-uploaded content that has been removed from our servers months ago, sometimes years ago. A lot of companies also forget to mention what they want removed, or better yet send us notices giving links to other domains we do not own, do not control and are not affiliated with in any way; while this is mostly human error, we had one company respond to us that they expect us to remove the content regardless... yeah, let me just hack that other server real quick for you...