...but look, this is exactly the point I'm making: If I want to run a sandbox or hexcrawl, where is the support from the game itself rather than a reliance on me knowing what I'm doing?
It's in the design not being so fragile that making a mistake will actually end your campaign.
Nothing I've said to do requires advice outside that found in the 5th edition PHB, DMG, and MM.
Could there be more "how to run a game"? Certainly, but since running a good game is something so easy that 10-12 year olds can manage it without even as much assistance is present in the 5th edition of the game, it's not really something that is a "must have" in order for someone to figure out how to run a game - and since the larger portion of being a good DM is playing to your audience, advice can actually be more harm than good because the guy giving the advice (even me) doesn't know
your group.
What if I want to run an episodic game? You're telling me that I'm doing it wrong and I should run a sandbox.
No, I'm not. You want an episodic game, run an episodic game - that has nothing to do with whether you run an episodic game while stressing over encounter balance numbers or you run an episodic game while being entirely unconcerned with encounter-building guidance beyond CR < Party Level = Ok.
I'm just not seeing the GM tools, quality of life support or much else for any model of running the game. Ultimately I feel like with 5e if you don't already know what you're doing, you're SOL re: DM tools and supports.
And yet 5th edition is the most supportive of new DMs out of any edition of D&D to date, because it gives you some options, tells you what matters (that you and your group have fun), and empowers you to use what works and change what doesn't - including outright ignoring any advice or guidelines that aren't meshing with your style.
Most common: Low level character gets knocked to low HP, then eats a next max damage hit (or a crit) and and dies.
Maybe try the option, included by way of the support you claim doesn't exist, to use average damage instead of rolling it for monster attacks.
I use that option for speed and to increase player ability to accurately assess how threatening an enemy is - as a result I don't have the problem you describe.
Second most common (and all other deaths!): Player gets dropped early by a high alpha monster, rolls a 1 on a death save and dies.
I assume you meant to say that the character failed 3 death saves (whether by rolling them, or by damage being dealt to the dying character), So there is nothing to say there beyond that yes, if the DM intends to kill a character it is likely that the character will die.
I was intrested you said that you never intentionally go for the kill - often we find that the monsters will stop us from reviving our fallen team mates though because often they are standing on them in a situation in which they get dropped.
Characters that are dying are less of a threat than characters that aren't, so monsters preferentially attack conscious characters unless there is some clear reason like mindless creatures trying to eat, or because I'm meaning to show the creatures particular thorough intent to kill off the party (which is only very rarely, because goals that aren't "kill all enemies" tend to be a bit more dramatic and interesting).
But we're not forcing people to have a particular spell for game balance... right?
You are right, we are not forcing that.
My group only has characters that use healing magic in about half of our campaigns - the only difference is that in campaigns with healing characters present hit dice are used less frequently.