There are lots of ingredients out there that are touted to have antibacterial properties. These include things like honey, salt, and lots of essential oils and carrier oils.
While that’s all well and good, these things are not preservatives. Not even close. Honey, for instance, will last forever… on its own. If you mix it in some water and leave it out you’ll find it gets quite nasty, quite fast. Its antibacterial strength is in its purity, where its lack of water and high sugar concentration smothers bacteria. Once sufficiently diluted, this is no longer true. (The same is true for other syrups).
The same is true of salt; when used in high concentrations it’s a great preservative (used often to preserve meat), but you wouldn’t expect the teaspoon of salt you added to a batch of stew to preserve it indefinitely.
The gist of this is to say that just because something is antibacterial/has antibacterial preservatives on its own in no way means that it will bring those properties over to a final product in any meaningful shelf-life-extending way. That’s what broad spectrum preservatives are for.