I'm not a big fan of zombie flicks. I've watched a bunch of them (I've done audio post on a few, so needed some references) and haven't found many I would go back and watch again. They are fun ti work on as an audio post guy; I get to do lots of vegetable abuse, etc.
Yeah I think there is no doubt they can be great, or at least great-ish. I think it should be uncontroversial to say that The Walking Dead has at the least moments or stretches of great-ishness. Another fine example of great-ishness is Train to Busan. If you haven't seen TtB yet, do yourself a favor and see it. If TtB does not move you, then check to be sure you're not a robot.
And there are others worth mentioning.
I would suggest the good thing these examples get right, as so much of storytelling in general is about, is their theme, which is: the importance of family and friends and sticking together.
I love a good zombie movie. Been a fan since I first saw "Night of the Living Dead".
I believe a zombie film can be great. There doesn't seem to be anything specific to the genre that would stop a great director from making a great film from a great script. richy's example is a good one.
I am a long time zombie fan but that said, I don't LOVE many of them lol. Night of the Living Dead, Dawn of the dead and Return of the Living Dead 1 and Two are my list of favorites and I will give a zombie movie a watch just to see if they can pull it off but in recent years i was surprised by The Battery which became one of my all around favorite movies and a few weeks ago I watched The Night Eats The World and was very impressed.
It's very easy to mess up zombies so when I find a good one I cherish it lol.