Suppose the maths, or some other rule, was changed which meant that a PC who goes down stays down, but is not at any greater risk of dying. That would increase the tension, without inviting the additional piling on of pressure that risks TPKing. Which to me shows that this is a system issue.
Of course there's a design reason for the yo-yo, namely, that it reduces the number of turns missed by players in combat. So the system issue may not be easy to fix while holding some of the key 5e parameters constant.