It is a risk. Slightly. But the character has three death saves to give, which represents a lot of wasted damage if you DON’T finish them off.We just don't have this yoyo problem, or see it as one. Couple of reasons;
1) Most enemies are smart. If the party waits to heal when they drop to 0, foes start to attack those who are at zero to keep them down. Which means now the party is risking character death.
And a lot of enemies aren’t that smart, to be able to suss out a potential healer while fighting for their own lives in six second rounds.
Cure wounds is not the problem. If everyone in the party who can have healing word isn’t taking it, they are doing it wrong. Our party also has an artificer (arcane jolt) and mercy monk (healing hands), both of which add to on demand healing.2) We don't agree about it being better action economy to wait. Cure Wounds still takes an action.
As do we. In general, this helps the party.3) We use random initiative each round, so you can't plan ahead as reliably.
This makes a difference; similar to us using critical wounds.4) We use lingering Wounds from the DMG.