I've always had remarkable results with loose teeth, and especially with coconut oil. My slightly loose teeth feel like they're cemented into the gums after a single pull. After regular oil pulling you'll find your problem with loose teeth just goes away, even if you're not pulling every day.
I'm surprised you haven't noticed anything so far. No idea how it would to with very or even moderately loose teeth, but OP is fantastic at rooting teeth to the gums.
Awhile ago I had a filling come off and the tooth broke apart so much that no filling or crown could be put on. So I decided on an extraction. The dentist told me that after 2-3 weeks what's left of the tooth would easily come out with little digging or surgery.
I started pulling since I couldn't get back that soon and instead waited closer to a year to make the appointment. Unfortunately I didn't stop pulling before the appointment and even after a year, they had to go in for surgery since the tooth fragments were still so deeply rooted to the gums.