In my work (which earns me $$ and puts me under a roof and puts bread and butter on my table), I almost never used a light meter in the studio.
The reason is that my customers are the average Beng and Lian who aren't too bothered to look at an image and comment on the number of stops difference between this part and that part of the image. All they really care is their faces look good, quite evenly lit from cheek to cheek, forehead to chin, and that's all.
However, if I was going to do silhouettes or "arty" lighting, then a light meter would be nice to have around, even though if shooting with digital. With film, I'm sure most would say it's essential, and not "nice to have around".
The playback on the LCD on your digital camera should not be used to assess/analyse simply because it's brightness can be adjusted. I have been told to use the histogram to do that but I'm still not totally comfy with the histogram. Each and every scene captured is different, and the histogram would also be different.
For example, if you shoot the same person in the same clothes and in the same composition against a black backdrop and white backdrop, you would see that the histogram is different. Only a light meter would be able to tell you had the lights set up to have the "correct" or desired exposure level for your subject.
In my work place, I don't use a light meter because my customers are only face-conscious and aren't gonna put a drill up my behind for the lack of precision. Besides, I have gotten used to the feedback I see on the DSLR's LCD. I know if the image is under or over.
In my own private play, I'm a bit more thorough, and use a light meter to measure left, right, up, down and all over.
Is it a must? It's up to you.
Besides, a light meter is not only useable in the studio. It's useable outdoors as well.