If you have to go out into the world and function at any level at all, it's impossible. People who manage to stay on hunger strikes for any length of time are generally institutionalized in some way, or else have helpers who keep a roof over their heads while they lie in bed. I once substantially quit eating and drinking for a couple of months, to the point where I lost 50 lbs and my pee turned black from dehydration. I did this by going to bed and just staying there. Dehydration makes you tired and groggy, so I slept through most of it. This was only possible because I am on disability and live with relatives who 1) won't evict me and 2) are slow to call 911 on me. Most people aren't in a situation like that. (This was not a deliberate attempt to ctb, incidentally. It was closer to catatonic stupor. It took no willpower to do because I barely knew what was going on.)
I was also anorexic as a teenager, and I found I absolutely could not drop below 300 calories a day without having bad physical and psychological symptoms that attracted unwanted attention. I lost the ability to climb the stairs in my 3-story school, for one thing. I'd have to stop and sit down all the time to keep from blacking out. I also frequently got weird cold sweats, where sweat beads would drop off me even though I was sitting still and doing nothing. This was all very distracting, and I couldn't pay attention to anything for shit. I almost failed the tenth grade, and most people's jobs are more demanding than my high school was.
Starvation can also have unwelcome long-term mental effects on people, even if going without food was voluntary and/or only lasted a few weeks or months. Some people who've gone through a significant period of hunger feel compelled to squirrel food away in strange places, where it may spoil or attract pests. Some feel a powerful compulsion to eat non-food items, a condition called pica. I went bonkers and ate a bunch of bird seed once. Why? I have no idea. I've had strong urges to eat sand even as an adult. Some go from a period of not eating to being unable to stop eating, to the point where people's stomachs have actually ruptured. Others avoid that but go from underweight to obese. It's easy to have that happen, because starvation shoots your metabolism all to hell.
So yeah, starving yourself is impractical and excruciating, and if you don't die (which you probably won't), you may be left with permanent physical and mental problems.