I've been here for 5 years, several neighbors have moved in and out, and only one went through that ritual for me. Few care in cold, impersonal Tokyo. It's not mandatory.
Yeah, it's different pretty much everywhere other than Tokyo. I'm just saying you can get away without it here, and it's not the end of the world. Moving to Japan for the first time is stressful enough already, I skipped it myself. But I'll definitely do it next time I move :)