My understanding of dutch roll (from watching a few flying videos on youtube and reading the wikipedia article) makes it seem like dealing with it is basic flight control coordination that shouldn't give a pilot experienced in a given aircraft any trouble.

Is it harder than I'm imagining in big jets, or in specific aircraft due to peculiarities of their handling characteristics?

Dutch roll is an oscillatory mode resulting from delayed cross-axis coupling and different axis stability. There's not really much a pilot can do about it other than trying to avoid exciting it.

Aircraft with swept, low wings exhibit dutch roll worse than other types (e.g. airliners). It's also worse at high speeds and high altitudes.

Yaw dampers vary based on aircraft and flight regime to "attenuating somewhat that annoying-bouncing-back-and-forth-feeling in the back of an airliner during cruise (imagine how bad it would be without active damping!)" to "preventing an oscillation from building in 2-3 cycles to a point where it will cause structural failure".

I think some of my confusion here was related to some notable youtubers misusing the term to mean a roll-on-heading exercise. When I wrote my last question, I was thinking "there's too much, or an unpredictable amount of adverse yaw", but I now understand the problem as "the aircraft enters a self-reinforcing oscillation in response to certain poorly coordinated control inputs", which doesn't sound like a good thing at all.

Thanks for all your input in this discussion. I find both flight in general and the case of the 737 MAX fascinating. Previously the implementation of MCAS sounded absolutely insane to me, but I can mostly understand how they got there after reading your comments.