From what I\'ve learned so far, the purpose of tokens is to prevent an attacker from forging a form submission.
For example, if a website had a form that input added
Yes. In general, you need to secure your login forms from CSRF attacks just as any other.
Otherwise your site is vulnerable to a sort of "trusted domain phishing" attack. In short, a CSRF-vulnerable login page enables an attacker to share a user account with the victim.
The vulnerability plays out like this:
As a pertinent example, consider YouTube. YouTube allowed users to see a record of "their own" viewing history, and their login form was CSRF-vulnerable! So as a result, an attacker could set up an account with a password they knew, log the victim into YouTube using that account — stalking what videos the victim was watching.
There's some discussion in this comment thread that implies it could "only" be used for privacy violations like that. Perhaps, but to quote the section in Wikipedia's CSRF article:
Login CSRF makes various novel attacks possible; for instance, an attacker can later log in to the site with his legitimate credentials and view private information like activity history that has been saved in the account.
Emphasis on "novel attacks". Imagine the impact of a phishing attack against your users, and then imagine said phishing attack working via the user's own trusted bookmark to your site! The paper linked in the aforementioned comment thread gives several examples that go beyond simple privacy attacks.