@Douglas B. Many have tried and many have failed with what your describing, I have a friend in Oregon that bought a 80 unit buidling in Memphis,, I told him don't do it.. " he basically said the exact same thing as you" give the tenant a quality unit try to get the best tenant etc etc.. Well they just sold and lost 400k on that one. they did all the rehab put in new play structure ( destroyed within 2 weeks. ) Bball hoops destroyed in a week.. BBG pits fights and shootings when the tenants went at it....
Personally I think if you want those really cheap type units you need to get out into the country.. find small little towns ( they are all over the midwest) Rents will be much lower but you will probably get them and your properties won't get trashed.
I have done some bizz in Kokomo IN.. thats a nice little city an hour from big city. nothing much happens but. I have never had a break in or any of the other issues you get from inner city Section 8... But I guess if you can live there and handle it you can give it a go.. those that live out of state and try it by and large get wiped out over time