Most of the time I brush my teeth, I do so on the can. As such, I cannot easily void my mouth at the end of brushing.
Just looking at it from the perspective of keeping the end product in my mouth for a minute or more, is this good bad or indifferent to my mouth? I.e. is this combination of toothpaste and saliva somehow bad for my teeth, or could keeping this fluoridated mixture somehow give me more protection, or won’t it matter?
On a recent visit to my new dentist, she actually recommended to me not to rinse out the remaining toothpaste after brushing my teeth. Her recommended order of mouth-hygiene-related activities had me floss first, then use mouthwash, and then brush my teeth without rinsing. I haven’t been following her suggestion as I dislike keeping the toothpaste/saliva mixture in my mouth; it just feels like I need to rinse it out and feel clean.
While this post doesn’t directly answer your question, it indicates that at least one dentist would probably have no problems with it.
Aside from the physical agitation, I don’t see much difference between holding brush-water in your mouth for a few minutes and brushing for a few more minutes.
It might arguably be better for your teeth. Special high-fluoride toothpastes specify that you should expectorate but not rinse (or eat or drink for 30 minutes) to give the fluoride a chance to do its thing. You wake up with a horrible taste in your mouth, though.
I learned in college that sitting on the toilet while expelling in the bathtub was the most efficient method when two ends of my body demanded evacuation simultaneously.