Some interesting opinions here. While I would expect a high school student (even one of the most lazy) to take that extra step in tackling challenging homework, I'm not convinced that an elementary student would have much success flying solo should his/her teacher turn out to be "pathetic and useless".
I believe it's always good practice for parents to act as a guide for their children in regard to homework (and other aspects of life for that matter). Note I didn't say they should do the homework, and most of the time, they should not even have to sit with the child during homework time. I see no harm in occasionally checking to ensure the child is on tast, and/or that he/she is not frustrated with something particularly challenging. If something has stumped the student, guiding through possible solutions is far better than simply doing it for them....asking them leading questions is a great way to point them in a direction that will enable them to find solutions independently. This will help develop thinking and problem solving skills that they will be able to sharpen as they get older and will not need as much guidance.

I'm a firm believer in homework. It provides practice of what is done in the classroom. If a student returns homework that has some incorrect answers, it is a tool to tell the teacher where a potential problem may be. If all answers were correct because parents did too much "helping" then the teacher will not know that an adjustment may be necessary. Homework should not be an all evening endevour....but something that will reinforce skills taught in the classroom. Parents, give your child guidence, yet the space they need to discover their own strengths and weaknesses.
(my particular weakness is spelling!)

Maybe European children are able to start school in 1st grade with these problem solving and thinking skills already in tact. I have not seen that in U.S. children...but somehow, I think they will be just fine.