As a DM for my group I have found that I dislike that my players (understandably) let their characters drop to 0 before doing any healing which causes the yoyo effect.
A huge amount of the "0 HP yoyo" is because DMs aren't vicious at 0 HP.
In a typical encounter, someone at 0 HP can be
dead before anyone else gets to heal them.
Instead, we have DMs that build super-deadly 5 minute encounter day fights to be "exciting", and then treat PCs with kid gloves once they drop them to 0 HP to not kill the PC.
If a character at 0 HP surviving to be healed is a rare event, then PCs won't treat it as a yo-yo healing opportunity, because healing spells don't work on the dead. Revivify (or stronger magic) is the only option, costing a 300 gp diamond, a full action, and touch range.
Then by late T2/T3 you start having foes that steal, damage or destroy corpses.
Doing "double tap" or in other ways actively trying to finish a PC without giving some heads up what is at stake is not something I want to do.
Thus, 0 HP isn't threatening enough to avoid. So you added mechanics to up its threat again.
Trust me, if double-tap is common, your "wait to heal until they have 0 HP" goes away. In fact, PCs are likely to start fleeing when at low HP because they fear being dropped to 0 HP. Because 0 HP is a prelude to rolling a new PC, not getting up next turn slowed.