I think it depends on how it's served. My mother was a wonderful mum but what she did with cabbage and silverbeet was an abomination - boiled to slime stage. I steadfastedly refused to eat it as a child and meals were a battleground.
With my own children who didnt much like vegetables, I tried a different approach. I grated carrot and really finely diced celery into lean mince for cottage pie and spaghetti bolognaise. I experimented with vegetables they were okay with such as green peas. My youngest doesn't like raw tomatoes at all so he got the tiniest bit. At one stage I hid a small amount of cooked cauliflower puree in the mashed potatoes.
I accept my sons are possibly never going to eat asparagus. I just serve my youngest peas if we are eating it. I didn't force them to clear their plate but encouraged them to have a mouthful at least.
A lot of vegetables are more palatable roasted with a little oil - I cut up potatoes, kumara, carrots, parsnips, a few onions split into quarters or eighth, a clove of garlic crushed in and enough olive oil to coat - best to mixing with hands. I put non stick foil at the bottom of the roasting dish to make clean up easy and put it in the oven for about 40 minutes at 200 degrees, turning vegetables half way through. Stir fries are another good way of getting them to eat vegetables. Just make sure stuff is tiny - my brocoli is just tiny - no big stalk bits, just tiny florets, my carrots are slim batons etc.
I discovered one son liked coleslaw and what could be healthier than raw cabbage. Also, if I am using frozen peas I just pop them into a cup - no added water - put a side plate on top and microwave for 1-2 minutes. They come out tasting very fresh and not overcooked and with minimal clean up.
You can also sneak vegetables into say a chicken pie. Sticking a bit of pastry on something can increase the chances of them eating it. Homemade pizza has some possibilities for increasing vegetable content. Or if they can be persuaded to eat vegetable soup - doesn't have to be homemade. My children liked pumpkin soup. A lot of children like baked beans - you could do a baked or microwaved potato and do topping of a small amount of baked beans or just serve them as the vegetable.
I just had to accept my children were never going to like raw tomato - okay with it in pasta sauce though. But they were fine with diced red or yellow capsicum with lettuce and Italian dressing.
My eldest grew up to be a vegetarian!