I'm reading this without reading any replies as I don't want to color my first reaction.
DMing isn't a job. It's just a different role within the hobby itself. Just like some characters might be a tank or support.
Everyone at the table is responsible for everyone's fun, so yes, you have an equal share of that as everybody. That said, the role you've picked does have more opportunities to increase both your fun and others.
As a DM, I am a cheerleader of the players. That doesn't mean going easy on their characters - player goals are to have fun. Character goals are different. They are often conflated, at least partially because in a combat-oriented game, the penalty for failing (character death) also leads to player losing (reduction of fun). Depending on the group, the opposite is true - pushing the characters hard so they feel the tension and overcome the risk leaves them the best reward. Plus good stories to tell others. So I may prepare deadly-deadly scenarios, but I'm also there ready to "say yes" to ideas and adjudicate if your cleverness will work. I'm not affraid to kill characters and roll in the open, but it happens very rarely. Last campaign I completed had one death, out of combat, as a martyr sacrifice to save another character. And that was because the player wanted to retire their first character.
Another comment on being a cheerleader of the players. I run the rules fairly and consistantly, but I would never descibe an important part of my job as being a "neutral arbiter". A referee in a sports match needs to be neutral and not favor either team. However, as hobbyists sitting around the table we are all on the same team. With only one team, we should all be on each other's side working for fun. The characters are working to overcome challenges, and there I will be fair, and often what I design is mean or deadly. But that's nto because I want the players to not have fun, it's because I want the players to have loads of fun trying to overcome them. Character failure just leads to another branch of the story, and all of the branchs - with character success or character failure - should be fun for the players and the DM.
I provide challenges, I listen to the players for what interests them and put more of it in. I let players add to the world and the narrative where it doesn't not cause issues with other parts, and craft a world and a story together. Many stories, actually - I make sure there are arcs for all of the characters that I wind around the other parts.
As an example of this, the first page of my "session prep" document is a list of the characters with notible skills, interests, etc. I scan it before plannign sessions, seeing if there are things I haven't fit in for a while that would work in this session. "Hmm, there hasn't been any traps or locks for the rogue recently, and we really haven't seen the elf's hatred of giants come up. What can I do with that?"
I do feel responsible for the world and preparing adventures. I do it completely homebrew, because that's a large part of the fun for me. I don't enjoy running a module nearly as much. I have so many world ideas I have a file with just setting after setting - I'll never be able to run all of them. At the beginning of a campaign I'll have ideas up through Act II - which may or may not be realized depending on the player's interest and the characters actions. I don't play "here's how I want it to end" - the players should have such an affect on the plot and the world it's hubris or railroading to try to work that out besides in the most general terms. I practice "Schrodinger's Plot" - nothing is true until it actually hits the table and everythign that hasn't cna change as long as it doesn't invalidate anything. I'm not afraid to kill my darlings if they won't work out, or rather leave them to wither on the vine if you'll forgive my mixed metaphor.
Every campaign I've run since 3ed came out has completed, with the shortest being four years. Before 3.0 I had run but nothing as coherent as a campaign - maybe a summer long superhero game here and module or homebrew adventures for friends.
Because I like to weave player interests in so much, I do not feel like I do my best work crafting one-shots. I'm uncomfortable with it, and also not accustomed to telling a full story in just a few hour. Just like writing short stories has it's own challenges and skills that only have partial overlap with writing a novel.
When players are learning or of different levels of skill I take as a responsibility to help them, even more than I do as a player.
I'm open to my rulings and calls being challenged. If it's slowing down play too much and not to dire (e.g. character death), I may tell the players I'm making an ruling for now to move on and we can address it out-of-session.
I've DMed some at conventions and it was a real learning experience - especially in seeing how players could enjoy different parts of our shared hobby than the groups I cut my teeth with. That said, I find I prefer running for heavy RP groups that treat the game seriously even as they joke and have fun within it.
I see the DM as having full authority inside the game world - as granted by the players who can revoke it if I abuse that trust. Outside the game I see the DM as one hobbyist among many.
So to conclude, as DM I voluntarily take on a role with more homework, but usually of the creative and fun type, where I work to present a living world with interesting arcs to the players so that together we can create something memorable through enjoyable sessions.
Being in a pure sandbox where you don't know which way to go or worse, it feels like random choice to go left or right, to me isn't much fun.
