In some areas beans on beans work. In others the fungus/ mold/ etc builds up and it is a real problem. Don't think you gave your location or conditions.
Corn on corn works better these days with the technology we have.
It is easy to plant corn into lightly worked bean stubble, your problem will be dealing with the corn stubble to put beans in.
I'll do beans on beans from time to time, but I'd be scared to plan it as a long term thing.
As well you are losing out on the buuilt up N the beans give you.
Alfalfa, you need to kill the old alfafla plants and let it sit for at least 3 good growing type months (a full year is better) so the auto-toxins go away. At 15 years old perhaps there are very few alfalfa plants left, but they will make a 2 foot circle around each plant that will not want to sprout a new alfalfa seedling.....
Seeding alfalfa in spring and catch the rains is good, the weeds will outgrow them but clip it & good to go.
Of late they have been planting in fall, late August 'here' and catching the fall rains, less weeds and makes a great start for the alfala next year, full crop.