It depends of the game in question but I enjoy drama as a tool to develop and humanize characters and make me care about them and their stories. I don't mind drama as a central theme or even being the core of a story but the thing about it is... it must be good drama. And by that I mean, for me it has to be logical, coherent, credible, and you also have to be careful to not break the suspension of disbelief, and thus, inmersion.
Just to give a well-know example, good drama (along with polyamory) was what I loved about Acting Lessons, and many people loved it too. But then, cheap drama (I don't wanna raise controversy, but... unpopular opinion incoming!) drove me away from it. But also, the fact that drama disrupted the polyamory premise. I didn't finish it and I intend to keep my gameplay that way: unfinished.
You see, as I see it, when you make a plot, start a game and set a context and a theme, you are making promises to the player, explicit and implicit ones such as: This game is partly light-hearted. But in this game ugly but plausible things can happen. This game is letting you choose even in a trivial situation between option A, option B, option C [both A and B] and option D [None]. This game takes in consideration what you choose and your choices impact the plot.
You need to be coherent about the explicit promises you make, be aware too about the implicit promises between the lines in case you do not want to give them for granted (And, in that case, get rid of them)... And then you should aim to fulfill your side of the contract. Is hard, but again, writing a good story is hard, especially when you try to mix naturally disharmonius themes such as tragedy and fapping. If you don't deliver what you promised, you risk players feeling sorta betrayed and that is sorta bad, unless that was exactly what you intended in the first place.
Also, be aware, 'reality surpasses fiction'. This is not just a saying, it's the fucking truth, and it has a reason to that. Coincidences are real, but you use it to solve a conflict in your story and, poof! suddenly is a deus ex machina and everyone recognizes it as cheap writing.
It's the same in reverse. You have a common story you can relate, with horrible but recognizable shit. Then, a calamity pops out of nowere, and it doesn't match the theme you presented. Boy, if you want to break inmersion it has to be a goddamn hell of a brilliant plot twist or you risk ending with 'Daenerys, Breaker of chains burning alive a city of innocent hostages when the battle is already won.' just because, fuck continuity, let's impact the audience in a way nobody expect.
To give you an example of what I mean: There's a game I enjoy, Alexandra. It doesn't give the player a lot of agency. It also has a Poly relationship with the main girl and her (girl)friend. And it's not really as dark in terms of gameplay as the premise is presented to us at the start of the game, or the themes and topics in it. I absolutely love the love interests the game offers you and I would hate them to be, I dunno, suddenly murdered. But I would not feel betrayed if that were to happen, even if it doesn't match with the current line of the plot, just because is a mafia themed game and because it begins with blood and violence.
But coming back to drama, and the game I put as example earlier, A LOT OF PEOPLE LOVED ACTING LESSONS TILL THE END and consider it a masterpiece, even if some others like me didn't want to even touch with a stick the next game by the dev when it came out. So, don't despair. Even widely disliked games have their faithful and loyal audience, and drama is fairly well-received in the adult game community, I think. More, at least than RPG games, anyways. ;P