Actually the spell says "once" not "while".
Once you possess a creature’s body, you control it. Your game statistics are replaced by the statistics of the creature, though you retain your alignment and your Intelligence, Wisdom, and Charisma scores. You retain the benefit of your own class features. If the target has any class levels, you can’t use any of its class features.
Nothing in the spell description says you stop using the creature's stats when you leave the body. By your own argument, this means you don't even need to be a Necromancer to get a permanent HP boost, as well as a permanent Strength boost, Dexterity boost, Constitution boost, special senses like Blindsight, etc.
Obviously no sane DM will ever adopt this interpretation because it's clearly not what Magic Jar is saying.