Not a problem with it being permanent ... other than, well, it's permanent. If you are sure about the location, sure, why not?
For the cross members, I prefer to use 2x6. But this is dependent upon spans as well (mine are 8') ... 2x4 will be fine for short spans.
Another useful recommendation, space the beams so that a frame will fit between ... instant frame rest between your hives.
Here is a picture of one of my stands where you can more or less see the construction and see a hanging frame:
This one was too tall, but otherwise served me well.