their way of doing "Almost shakespearean" was to have Donte repeatedly spout "fuck you"
Invoking Shakespeare was pretty idiotic on their part, yeah. But I rather enjoyed the infamous fuck you->no fuck you->no fuck YOU->vomit exchange, and probably not for the reasons you might think.
The demons in DmC have essentially won. They're not struggling for anything, they're not at war with anyone. They're in charge. They've been in charge for a long time. They've grown arrogant, yes, but that trait is not unusual in game antagonists. They've also grown fat and lazy. They've grown dull. They haven't had to use their wit, cunning or imagination in centuries, if they ever had any to begin with. Their minions are ugly misshapen things wielding crude weapons; they're not very good at combat because they can only manifest in Limbo and they haven't had anyone to fight in there in who knows how long. The Succubus ends up being little more than a purulent, bloated organ whose very sentience is irrelevant to its task.
Now Dante comes in. He's not an experienced professional, hired by a client to perform a job he (initially) has no personal stake in. He's an angry kid on a revenge quest whose current goal is to kick the hornet's nest.
Of course they're gonna shout FUCK YOU at each other. That's the only possible way their interaction could have gone down. On that level, it was realized perfectly. Given the setup, I was actually impressed that whoever wrote that scene took it all the way there. Was it childish, crude, and dumb? Yes, of course it was. Exactly.
That said, I get it. A whole lot of people don't want Dante to be an angry upstart, and they want him to fight elegant fiends trying to upset to status quo rather than trying to maintain it, possessed of might and grace, who have the courtesy to say nothing if they have nothing to say. That's legitimate. If I had any attachment to the prior series then I would be pissed off too, and I sure wouldn't try to change your mind if you hated it, because I can totally understand your point of view.