"If I understand correctly, then anyone with certain authority can file a DMCA takedown notice, which results in the removal of protected content. Anyone who posted the content and wants to challenge that notice can also do so, resulting in the restoration of the content, but not until a few days later."

No. Anyone. Period.

"In the long run, this mechanism does not suppress free speech or prevent the information from being distributed if proper counters are filed. However, in the short term it can delay that distribution. This is still potentially significant, but it is a different situation."

Again incorrect. DMCA states that to file a counter notice, you are allowing the DMCA violation filer to go after you in court in their country. So if I am from France and post an article about The Church of Scientology, to counter the DMCA I would have to allow TCOS to sue me in US courts, not in my country's courts. The reason I mention TCOS is because they abused DMCA a few years back silencing most information online giving them negative PR. Only few actually filed counter notices.

In general most people don't file counter-notices because their are either scared about legal procedings or don't know what part hit the DMCA clause, don't want to be taken to court (remember the DMCA notice does not mean the person even knows who you are, they just got information forwarded through the ISP or whatever service) while the counter notice reveals who you are.