I think your heart is in the right place and you plan sounds reasonable. No need to seek the MBA to get into law enforement (unless you just want it first)
21 is still pretty young and there will be plenty of crime available for you to fight, no matter when you enter the field.
Best advice I can offer is to 'be there' 100% for whoever you work for. Don't take a job at a local PD with your eye on the door looking only to use it for experience. It will lead you put out an air of being too good for them - and no one like that
Good luck and keep on the path
"Those who would give up essential Liberty, to purchase a little temporary Safety, deserve neither Liberty nor Safety."
Benjamin Franklin, 1755
"Living in our society is like living in a very tall building. The rich live on the top floors. The poor live on the lowest floors. And only the cops travel to all the floors. Only the cops see it all."
Det. Ted O'Conner - Chicago P.D