I... would like to sign up but I can't because I don't want to use Facebook, Google or Twitter. Can I just give you my email and you send the login token per email instead of through a third party?
You also mention fake accounts: I don't know what this site does (I wanted to filter on a field and it told me I needed to login for that, not sure how a fake account would help me defraud the owner using that) but I would hope that random website owners can't tell Google/Twitter/Facebook about how naughty I've been and get me banned from Google/Twitter/Facebook. Therefore, the site owner will still have to ban spammers that created a Google account, same as they have to ban spammers that created an email address.
Every time I've tried to implement a third party login, it has been quite a pain. "First party user system" is a fancy word for what is actually the simplest option. At least to me, as a developer, so I don't see the advantage from that perspective either.
I totally get it from your point of view, but whenever I make passion projects - if I don't have to build user management features in terms of passwords - it's a big load off my plate.
"Therefore, the site owner will still have to ban spammers that created a Google account, same as they have to ban spammers that created an email address."
Sure, but instead of trying to be better than Facebook/Twitter/Google at making it hard to create spam/fraud accounts you simply have to block the ones that get through the already best systems in the world. You don't need to track IPs, fingerprint patterns, phone numbers, emails, etc to try to filter out automated systems the 3rd party does it for you and is always getting better with 0 effort on your part.
It's also frees you from ever needing to ask for more information than needed. Don't need their phone number? Great, you'll never leak it because you don't need to request it from the 3rd party or user or account when requesting the token. Just have a token instead of a password? Great, if the user practiced poor password security Google/Facebook/Twitter are more likely to block suspicious logins than you ever were AND you don't have to reset their password and send them an email, the 3rd party will. Also tokens auto expire/renew as part of the app logic, down to minutes if you want, all without bothering the user.
If you've tried to implement 3rd party logins as additional steps to your already first party system you don't really gain any of these benefits . If it's all you implement it can save quite a bit of work.
In the end though nobody should be changing your mind, it's you that should explain why the developers should support a 1st party only system and turn away those that don't want to create yet another web account or why they should support both and the associated burden for the 1% that won't login via 3rd party.