By what you are saying it seems that you really don't need a barbell either. Accually you don't need to buy any weights at all you could just 'do it like a caveman' and move stones around to build strength. Technically you still are a weightlifter :)You also don't need a bench. Plenty of work to be done without it. Even heavy chest can be done with weighted dips. The best back exercises don't require a bench. Arms and shoulders don't need a bench. Legs don't need a bench.
Also I don't know of any weightlifters who dont do any bench press. There are ways to get around using a bench but it is inconvenient and removes some exercises including some important ones.
What if its time to change up your routine and you need 'normal' squats? What if all you want to do is press weight from the sticking point in your squats? What about people who don't want to have to work their grip to squat. It seems to be more trouble than its worth not to own one.If you're worried about failure on the squat, you can do Front Squat, Hack Squat, or DB Squats as heavy as you like with no fear and no need for a cage.
So technically there is no mandatory equiptment including owning plates, bars, etc but since no one wants to go to an extreme such as picking up boulders to get stronger a bench and a cage are high priority peices of equiptment.