A269 It makes sense that if a suffocating creature fails death saving throws, it dies. But what happens if the creature succeeds on the death saving throws (while still not being able to breathe)? According to the death saving throws rules, the creature would become stable. But according to the suffocating rules, the creature can't be stabilized until it can breathe. So there's a contradiction.
If you resolve the contradiction by specific (suffocation) beats general (death saving throws) then there's no point in making death saving throws because successful saving throws are useless.
I think the problem is that the only two mechanics for "dying" are death saving throws and massive damage and neither works in the case of suffocation.