You can do exactly what you propose. The result will be flour-thickened milk. It is not the same thing as a bechamel sauce, because it tastes differently - you are missing all the fat, and your flour hasn't been fried. But nobody stops you from experimenting with it, and developing recipes with it if you would like to. (I am not aware of any classic recipes which use it). Also, you may want to look into using starch instead of flour for that application - it is easier to work with than non-fried flour.

If you want to make bechamel, a roux is necessary because, well, that's what bechamel is. If you use your proposed method (or anything else) then the result will not be a bechamel, per definition, and it will also taste differntly. In the first place, you will be missing all the fat, and then there are subtleties like the flour not being fried.

This doesn't have to stop you from using a flour-thickened milk, as you propose. Nobody stops you from experimenting with it, and developing recipes with it if you would like to. (I am not aware of any classic recipes which use it). Also, you may want to look into using starch instead of flour for that application - it is easier to work with than non-fried flour.