Most people don't leave toothpaste in contact with their teeth for long enough. My dentist recommends not rinsing after brushing, and just leaving the toothpaste in there.
(Fun aside: This is also the procedure on the ISS to avoid having to spit in zero gravity.)
Many people rinse with water afterwards. If I don't rinse I get a wicked stomach-ache almost immediately after swallowing some toothpaste residue, so I rinse
(Fun aside: This is also the procedure on the ISS to avoid having to spit in zero gravity.)