The tl;dr: If your toothpaste contains Flouride, it needs to stay on your teeth for 20-30 minutes in order to work properly. If you don't want to do that—or you don't have a toothpaste containing Flouride—you can followup the brushing with a Flouride-containing mouthwash, which you do not wash out.
This is what I do. I use a mouthwash with Flouride, and don't rinse my mouth for ~30 minutes after using it.
This reminds me of a change that my dentist's office made a few years ago: Apparently dental insurance (at least my plan) has added coverage for a Flouride treatment with every office visit, so they have me do a Flouride rinse—probably with a higher-concentration rinse—at the end of each visit.
This is what I do. I use a mouthwash with Flouride, and don't rinse my mouth for ~30 minutes after using it.
This reminds me of a change that my dentist's office made a few years ago: Apparently dental insurance (at least my plan) has added coverage for a Flouride treatment with every office visit, so they have me do a Flouride rinse—probably with a higher-concentration rinse—at the end of each visit.