Agreed. Anyone with even passing knowledge of shapechanging would know that fatal injury to the transformed person causes them to change back instead of dying. That's the kind of information (here is a danger, here is how you deal with that danger) that people eagerly spread and share. It isn't some hyper-technical rules point, it's a fundamental principle of how transformations work in the world.
3E had the right idea here: There's polymorph, which is a spell to be cast on a willing ally for buff or utility purposes, and there's baleful polymorph, which is a spell to trap an enemy in animal form. I don't know that I would split polymorph into two spells, but I would give it two modes:
The regular mode requires a willing target and is otherwise the same as now.
The baleful mode is limited to CR 0 forms. You keep your own hit point total and don't revert when reduced to zero. You get an initial saving throw to resist, and another save at the end of each of your turns. On a successful save, the effect ends. If you fail three saving throws, the transformation becomes permanent until dispelled.