No but a robot that does the dishes needs to know how to know what a dish is and how to clean all different types and what's not a dish. The complexity of behavior needed to automate human tasks that cannot be done by a assembly line robot is immense. Most manual labor jobs are still manual labor because they are too full of unknowns and nuances for a simple logic diagram to be of any use. So yes some robots need to understand what's going on

And as for parroting vs remembering current LLMs are very limited in the capacity of creating new things but they can create novel things bash smashing together their training data. Think about it, that's all humans are too. A result of our training data. If I took away every single one of your sense since the day you where born and removed your ability to remember anything you wouldn't be very intelligent either. With no inputs youcould produce no outputs other than gibberish which an AI can do to. ( And I mean ALL senses you have no form of connection with the outside world )