Agreed. I have an eleven year old daughter, and I'm constantly quoting the movie version of Alfred Pennyworth to her, in the perennial hope that some day it will just click.
"And why do we fall Master Bruce?"
"So we can learn to pick ourselves up."
I like to think that I've done well, letting her get into programs that she finds worthwhile, hoping that she'll apply herself in a way I never did at her age. It's painful watching children fall in and out of like with things when they realize how much work is involved, but having given her exposure to enough things, I've found that when she can grasp onto the kernel of something she truly enjoys, it's a lot easier for her to overlook the effort involved.
It doesn't fix the fact that some things aren't worth trying for (especially eating her Spinach, though that one's obviously not crucial), but then you have to overlook that y'know, she's eleven, and if I'm honest with myself, she's a million times better at applying herself than I ever was at her age.
The only thing I've found that works is when there are crises, we try to collectively break down the problem into its smallest component parts, and deal with them in very small chunks. Another very useful tool has been the "Destination Imagination" program -- I don't know how old your kids are, or whether the program is available in your school district, but it is, specifically, an unstructured lesson in getting kids to learn creative problem solving through small, focused problems that they are challenged to solve (like how to most efficiently roll golf balls into a bucket on the other side of the room using a broom, two chairs, a pack of bendy straws, etc.)
Having been a judge for DI, I can assure you that the children came up with a variety of solutions I never would have fathomed, to varying (but often impressive) degrees of success.