I think clover and alfalfa will out compete each other ... one will dominate at the expense of the other. I have pulled alfalfa roots and not much else will draw that much.
Clover with chicory will give you balance and chicory will survive in tough low moisture summer conditions.
Also alfalfa is fussier to grow than clover or chicory. I know clover responds well and seems to grow better after it has been abused(light disking makes it take off).
I like chicory. I like clover. Best thing I've done for my clover is attack it with as much other stuff as possible, but annuals, so when the annuals are done, the clover can fill in those spots for the rest of the season. I've also got sedge. Still doing battle with it.