Frameworks have no idea how you intend to use the EM, so they cannot close it (except, may be, on finalization, which is not guaranteed). Yes, not closing them would create a resource leak.
The idea is the same as "always close java.sql.Connection" (despite some data sources have settings to close them automatically by inactivity) or "always close Hibernate session".
Besides, if you plan to write portable code, you shouldn't rely on specific JPA provider "being smart" -- other may fail to close the EM in time.
If you created it using EntityManagerFactory you will have to close it no matter what framework you use.
If you obtained it using dependency injection (eg using EJB and @PersistenceContext annotation) you should not close it by hand (AFAIK it will cause RuntimeException).
I have obtained EntityManager using @PersistenceContext annotation in my repository. I can see that after the connectionpools reaches its maxPoolSize it does not get cleaned up.
However if I create EntityManager using EntityManagerFactory and call entitymanager.close() then connections are getting cleaned up. I am using c3p0 as connectionpool library.
Justo to give my 5 cents you must remember to close your EntityManagerFactory.
I was just using it to create my EntityManager and it opened and kept opend a new conection pool every time.