He doesn't have to & some of his regenerations have taken place outside the TARDIS. In "Planet of the Spiders", the Third Doctor left the TARDIS before regenerating into the Fourth Doctor. In "Logopolis", the Fourth Doctor was outside when he regenerated into the Fifth. The Seventh Doctor was in a hospital morgue when he regenerated into the Eighth in "Doctor Who", the TV movie.
When he can, he does tend to return to the TARDIS before regenerating. As he's said several times, regeneration is a traumatic experience: "like dying" ("The End of Time") & "it always hurts" ("Death of the Doctor" (Sarah Jane Adventures story)). Also, as explained in "The Impossible Astronaut", he's particularly vulnerable while regenerating. The TARDIS is his home -- familiar surroundings & a place of safety (as much as anywhere is & far more than most places are). He has every reason to take refuge there while regenerating.