To each their own - if your only goal is to minimize missing qualified people, then I would agree that you should offer FT offers to everyone. If you have a stronger goal of minimizing the number of unqualified people you hire, then that's a different issue.
Personally, I'd rather work at a company that falls into the latter category.
Yup. "No false positives" is my goal. I've experienced what happens when a company gets bloated and teams get diluted with bozos. Even one person can poison a team. Firing people is bad for a team too. I'm determined to avoid that to a great extent. I know of no other way than actually working with a person to determine whether I want to keep working with them.
I don't think most people even question how ridiculous it is that companies interview a person for a couple hours and then agree to work with them for many months or years before they will even consider firing them (usually only after additional months of trying to "work it out").
In my opinion the best recruitment tool is having a team that a potential candidate would be really happy (and lucky) to work with. You can only do that if you keep standards up and hire slowly and methodically. A bit of a pain in the beginning, but worth it for everyone involved in the end.
Does not giving someone a full-time offer after the short-term contract hurt the team like firing someone? I could imagine it going either way. Perhaps it's better because those not in their contract period don't start thinking "it could happen to me at any time."
Personally, I'd rather work at a company that falls into the latter category.