Are Zombies frightening anymore?
I'd say no, and never were, individually or in small groups. But they weren't really supposed to be frightening in and of themselves, their 'frightening' element was the extreme difficulty in killing one, the strong possibility a character may have, or did, know particular zombies, and the fact that any humans taken by zombies simply swell their ranks. It's ironic in that by most fiction, a medieval society has almost no real trouble putting down zombies but modern society does, our numbers and density work for zombies they can spread monstrously fast. Where in a medieval society a single guy in plate and chain with a mace can put down dozens without any danger of being bitten (and thus infected.)
Are they just a setting?
No, and yes. What they HAVE done is become oversaturated with the media. They're the metaphorical goblins or bumpy forehead aliens. People are starting to go "not this again". It is VERY hard to make them a believable threat especially in this day and age as technology increases and we're reaching a point where, ten, twenty years from now a "Zombie Apocalypse" would become totally unbelievable due to basic quarantine laws and the military's ability to project force against the Zombies with drones instead of lines of men who can in turn be turned by the Zombies.
As for too easy to kill, no, most fiction depicts zombies in "our time" has harder to kill than fantasy zombies because of our reliance on firearms. Most fantasy, a good sword to chop off their heads or a mace to bash them in coupled with much lower population densities (thus less zombies) made it much easier to kill them a few hundred years ago.
What sort of Zombies are they?
Too varied to really say anything meaningful on this.
How much of a plot is needed?
Honestly, I've never actually seen one that wasn't survival based when it comes to Zombies in a modern environ.