The common wisdom is that leek greens are so tough, they should only be used to make stock. I agree that leek greens are great to throw into stock, but that’s far from their only use. Yes, the fact is that they are tough. But you know what makes tough things tender? Cooking! Slicing them thinly across the grain of the leaf fibers also helps.
To make demonstrate my point, you can use leeks in one of the most tender of dishes, the French omelet. Here’s a photo walkthrough with captions.
Yes, there is a bit of chew in finely sliced leek greens with just 10 minutes of cooking. But that chew still works nicely in a custardy French omelet. If the leek greens are used in a dish that is going to simmer for 30 minutes or more, the greens would be that much more tender. And if the dish contains other ingredients with some “chew” the finely cut leek greens would blend right in.
Having said all of that, there is one case where you may choose to only use the white part of the leek. That’s if you are going to make a puree, such as a Cream of Anything Soup, and are using leeks as the aromatic, and you don’t want green to be part of the puree. Imagine a cream of butternut squash soup, which you want to have the nice, rich orange color of the squash. If you puree orange and green together, you end up with brown, so stick with white aromatics. But still, don’t throw away the leek greens. Use them in the next dish!