Just how important do you think having a good understanding of human anatomy and body shape is if you aim to be a cartoonist in this day and age?
very low, really
your popularity/social skills > your style > how many trends you follow > pandering to certain groups > "knowledge of anatomy and body"
Even if your end goal isn't to draw realistically, it's immensely helpful to understand how and why the body does what it does, and how it looks across a variety of people.
Even for a show like adventure time, if you take the good artists from it and asked them how much life drawing they did, the answer would be *tons*
Depends on what you think a "good understanding of human anatomy" means. You won't need to be a student of human anatomy (eg knowing every muscle, every bone, every realistic expression) unless you're planning to go into some high-budget studio, but you will have to be very familiar with how weight shifts itself around in the human body and how it looks from different angles if you plan to be in any animation position.
Also don't let the highly-stylized, minimalist designs of modern cartoons fool you, in terms of actual animation quality, the standards today are usually quite high.
it depends entirely on your subject matter and style
if you're drawing a heavily stylized version of reality, you still want to have basic anatomical knowledge (in other words even if your forearms are diamond shaped, you still want to put the 'sides' of the diamond where a forearm should be at its widest, and narrower at the wrist end, etc. Bruce Timm shit comes to mind)
If however you're just drawing geometric shapes with faces on them, then.. you have to study geometric shapes. Different, but just as important. I've tried drawing Finn a bunch of times and quickly realized that it doesn't matter how good I am with realistic people, I have to think 'cylinder' and get that shit right or he will look terrible.
All you need to get into the industry now n days is a CalArts degree.
You don't have to actually know how to draw. (and no, CalArts doesn't teach you how to draw, it teaches you how to make connections)
You may not use that knowledge of anatomy directly, but it's a vital part of learning.
An animator first learns life drawing for the same reason a cook first learns preexisting recipes and understands why they are good before making completely new ones.