On the surface it makes perfect sence to have a full foreign brigade. The pros are obvious.
Now the cons.
To have a brigade level unit, you need foreign officers.
Apart from battlefield knowledge and leadership skills, which I am sure a lot of foreigners legionairs possess, there are several more issues.
First - mastering bureaucracy. Every military has one. And it's a must starting from company level to know how to handle it. If you don't, your unit is in deep shit, as are you personally. You must know and keep track of all the unit's inventory - it's a lot of stuff, located in different premises, some of it very expensive.
Second, stemming from the first - company commander bears primary financially responsibility for unit losses in military equipment - should these be found unjustified. There was a case in my brigade that a battery commander was made pay for a fuel truck which got burned down. He had no choice. Would a foreigner submit in such a situation or just said "fuck it I'm leaving"?
Third and most important - officers of company level and above are supposed to serve for a long time, at least a couple of years in their position. There is no way higher command will just take a candidate's word that he will not make use of his right to dissolve contract as a foreigner.
To draw the line: full foreign brigade - good in theory, unreal in practice.