When my partner was on the blood thinner warfarin, he was told it wasn't true that he couldn't have spinach, kale etc (vitamin k rich foods). What was important is that if he chose to eat those foods, to make sure he gets around the same amount of vitamin k everyday. The main thing with blood thinners is keeping your vitamin k consistent in your body.

For example, you can't eat a good serving of spinach one day, then not have a vitamin k rich food again for a week or so. That plays havoc with your blood thinner.

So, it does involve educating yourself on the amounts of vitamin k in different foods which people often can't be bothered to do.
Also, a lot of people don't have any desire to have spinach, kale, or brussel sprouts etc every day, so it is just easier to cut them out totally or limit them.

Just wanted to let you know you can eat vitamin k rich foods if you really like them. Just eat some every day, rather than a large serving once a week. A dietitian could help you if necessary.
It is just easier for the doctor to tell you to avoid those foods. And that is fine advice if there is doubt the patient will educate themselves on incorporating a consistent amount of vitamin k in their diet everyday.

You may need more frequent blood tests as you transition to eating vitamin k rich foods as your blood thinner dose will change slightly.

Another option is to ask if a blood thinner like plavix (or generic) would be suitable for you, as there is no interaction with vitamin k.