The problem is alfalfa is expensive to transport (heavy due to desired moisture content). So while it can be cheaply grown in the Midwest, it can't be cheaply transported from the Midwest to where buyers of alfalfa are (typically overseas).

Alfalfa is also a staple for crop rotation, so any farming operation will still grow some alfalfa to maintain rotation for good soil health (or during bad condition seasons since it's hardier to poor conditions and not a permanent crop).

If alfalfa cannot be exported (through policy or economic conditions), the low price attracts more livestock production in-state (which would be even worse for water use).

Those things makes it a hard crop to target for sustainability and export.