Why is a roux necessary?
You do not need to make a roux. While your proposed technique of adding flour directly to milk will almost certainly lead to clumps, there are other ways to incorporate flour, butter, and milk: namely, a beurre manié.
First, let's explore why flour clumps in hot liquid. As explained in this Seattle Times cooking advice column, flour will immediately gelatinize when added -- forming a sort of gel-like barrier that encases clumps of flour. No amount of stirring will break up these clumps. A simple fix is to use Wondra or a similar product. This flour is specially formulated to avoid clumping; I am not familiar with the details of their process, but I know that the product can be directly whisked into a sauce without clumping. It is fairly popular in America for making gravies.
But, with standard flour, the best fix is to work in fat: it works as a lubricant, keeping particles of flour separated for long enough to incorporate into the sauce. As you know, one method to accomplish this is to make a roux: flour is added to hot fat and stirred until incorporated. Only then is liquid slowly added. An alternative is to make a beurre manié: a mix of cold butter and flour that is added, uncooked, to the sauce.
Both a roux and a beurre manié provide sufficient lubrication to prevent clumps; however, many chefs prefer roux for a variety of reasons.

Making a roux requires less mechanical action. Working cold flour and butter requires a lot of stirring or kneading. A roux, on the other hand, can be quickly whisked together with less resistance. This is ultimately a personal preferences: you may find one or the other workflow easier.

Some people think a beurre manié tastes &quot;floury&quot;. The hot butter in a roux lets you &quot;cook out&quot; the floury taste, some say. Not everyone agrees: this cook tried both methods, and in a taste test, saw no discernible difference. If a sauce thickened with beurre manié tastes good to you, go for it.

In the same vein, a roux lets you toast the flour. Dishes that use &quot;dark roux&quot; (like gumbos, etouffée, or Japanese curry) rely on this toasty flavor for depth, color, and balance. In this case, you cannot substitute a beurre manié without losing flavor.


The beurre manié has a bit of a bad reputation as a &quot;shortcut&quot; or inferior option to the roux. But, if you are struggling with roux, or just want to try a different process, I encourage you to give it a shot. If you do get some clumps, you can always just strain the sauce through a fine sieve.