Can your character be lost instantly to fickle dice rolls though?
It happened to me in a 4e game. (The character was revived but there was a phase where it looked like he might not. We were only level 3, IIRC.) If it can happen in the game people openly knocked for being too "safe" and having too high initial HP, it can happen anywhere.
(Very specifically we were fighting a solo. I was slightly above 25% HP and thought, as a Paladin, I could take a hit. The solo proceeded to crit on its strongest attack at exactly that moment. I went from over 25% HP to under -50% in a single hit, something all of us, DM included, genuinely thought wasn't possible. Dice were rolled open, this was Roll20, so no trickery involved. By 4e rules, that's literally instant death, no saves.)
The outcomes are the results of whole series of decisions you’ve made. Sure, random chance plays a role, but it is a secondary role to your own decisions.
Not always.
All of your actions are calculated risks (though I suppose maybe less calculated if your DM isn’t forthcoming with important information like DCs and potential consequences; that I could certainly see making deaths feel much more random).
I think it comes down to what we’re looking for from the game. You want to contribute to a narrative that the group constructs together. I want to exercise agency within a fictional space. The possibility of unexpected character death undermines your ability to construct a satisfying narrative, while the impossibility of the same undermines my sense of agency.
I guess I just see it as...you are exercising agency, but some of that agency is at the level of authorship.
And, as noted, I do not ABSOLUTELY prevent deaths. They coincidentally haven't happened yet, but if they did I would put them in. They just would be recoverable one way or another, unless the player didn't want to do that. Maybe they don't find the costs worth the benefit, maybe they want a new character, maybe they like the story impact of the death. But I won't lock a player out of continuing a story solely because
one tactical error and incredibly unfortunate dice said so.
Edit: That said, I also wouldn't let my players exploit my goodwill. This is meant as a gesture of respect between them and me, a collaboration to produce the best experience we can. If my "I won't arbitrarily end your story" is exploited to extract maximum advantage, I will become much less friendly about it. Death should always, always be a SERIOUS thing, even if it isn't a permanent thing. It should have consequences and be treated with respect. Will you be willing to pay the price? Will your friends? That's so much more interesting to me than "oh, yeah Bob died last year, it was pretty sad. Then we met Roberta."