It's a bit more complicated than that.
Google's system is optional for both the content creator and the rightsholder. If the rightsholder would prefer to use the DMCA, they obviously can. If the content creator would prefer the rightsholder use the DMCA, they can dispute+appeal which will force the rightsholder to file a DMCA takedown if they want to continue with their claim.
Unfortunately there's often a lot of confusion about the dispute+appeals process, since it's a multi-step process and there's a ton of people incorrectly conflating disputes with appeals, but the important takeaway is that a content creator can choose to force a DMCA takedown via an appeal (which happens after a rejected dispute).
The reason content creators rarely choose to go the route of forcing a DMCA takedown is because:
1) the only remedy for a DMCA takedown is a removal of the entire video, which is often less preferable than the remedies offered by the google process (ex: replacing/muting the audio in the claimed section, monetization split, restrictions in only some geographical regions)
2) the DMCA repeat infringers clause requires that companies terminate relationships with people that repeatedly get DMCA takedowns. This manifests on YouTube as a 3-strikes-and-your-channel-is-deleted policy that only applies to DMCA takedowns, but not copyright claims that come through the optional google process.
3) There's some scary warnings about how particularly vindictive rightsholders react to this by choosing to file a lawsuit against the creator in addition to filing the DMCA takedown