I don't think anyone finds arbitrary death fun
Is there any other kind unless the DM is actively seeking, planning to kill a PC? Characters die, it happens either because a player does something dumb, they get bad dice rolls, or they enter into a situation or combat that is above their abilities to survive.
It really does depend on your play style. In my style of play, no-one dies just because they get bad dice rolls, or just because they get in over their heads. That would be what I call arbitrary. In the style of game I run, it has to be a combination of things: Doing something you know is dangerous AND being dumb / unlucky, for example.
For me, unless a player has a chance to see that they are in danger and decide to risk it, I am taking away too much of their agency.
As a result, most of the character deaths in my games are enacted with the approval of the players. I've had characters die when ...
- ... they deliberately dived into deadly combats because they had an unhappy love life
- ... they sacrificed for the team (multiple times, very often involving explosives)
- ... their player wanted to play a new character (multiple times)
- ... they decided it would make a good story (moistly in storytelling games)
The last "unexpected" death was in my Pendragon game. I had established with the group that they were happy with the high risk of playing Pendragon, and the player adopted an aggressive stance versus some barbarians (this is a highly dangerous option). They critically failed their passion check and when downed, the healer critically failed to heal them. I asked the player if they wanted heroic GM measures to save them and they said no.
A combination of knowingly high risk activities and a lot of bad luck, but even then it was a player choice. That's about as close to arbitrary as I get.
To be clear, that's just the style I like. Not trying to claim that the arbitrary deaths you get in, for example, an Aliens campaign (which is often 2 bad rolls -> dead) is bad, just that there are other styles of play. It's a continuum where different people find fun at different points.