>>Ingesting toothpaste won’t kill you

Do NOT do this with tin (AKA 'stannous') fluoride toothpastes. Tin fluoride is *bad* for your joints, among other things. These days, you have to really search for stannous as it's not appropriate for kids (who sometimes swallow)

That said, yes, leave the toothpaste in your mouth as long as you can, and don't rinse after spitting, as with any fluoride it's good for remineralization.

But if you're interested in remineralization, google hydroxyapatite (a nano ceramic originally developed for bone healing) toothpaste. Although it was developed in the US, it's not available here - so I import mine. This is not a dental conspiracy, it's just that toothpastes here are regulated as a drug in the US, which means very expensive clinical trials for OTC.