I believe Kirk did graduate as a Lieutenant, in the prime universe he also graduated as a Lieutenant (TOS, "Obsession") and the Star Trek website also notes this that he achieved Ensign rank whilst at the academy in his FIRST year. Looks like accelerated career even in the prime universe.
Doctor Bashir in Emissary also joined DS9 straight out of the academy at Lt JG but as mentioned happens with Doctors in the real world. As an aside I'm certain in the real world Lt ranks are given after graduation in certain circumstances, I was actually offered this when applying to the UK Navy for engineering.
Lt to Captain isn't as bad as cadet and Lt's command small boats in the real world, although agreed a "captain" rank is ridiculous, just should have received the command instead