Why is it necessary to be able thicken a sauce with roux without making lumps if the going strained anyway?

You're right, if you're straining a sauce, lumps in the roux wouldn't be a problem. However, straining a sauce isn't always ideal, and here's why:

* Flavor and texture: Straining removes some of the flavor and texture that the roux contributes. This is especially true with browned roux, which imparts a rich, nutty flavor to the sauce.

* Nutrient loss: Straining can also remove valuable nutrients from the sauce.

* Effort and time: Straining takes extra time and effort.

Why is a smooth roux preferable?

Even if you plan to strain the sauce, a smooth roux is still preferable for the following reasons:

* Appearance: A smooth sauce is more visually appealing than one with lumps.

* Mouthfeel: A smooth sauce has a better mouthfeel and is more enjoyable to eat.

* Versatility: A smooth roux can be used in a wider variety of dishes, including those where straining isn't desired.

In summary:

While straining can address the problem of lumps in a roux, it's not always the ideal solution. A smooth roux is generally preferable for flavor, texture, appearance, and versatility.