I made the point in the
Civil Rights Game thread that this is, if anything, a question of outreach. Baseball has to prove itself an attractive pursuit early on for someone of any ethnicity to take it on as a career, and this requires the infrastructure of school teams, quality coaches, youth baseball leagues... There are many things baseball can do to broaden the pool of potential recruits by investing in the community.
Also, of course, I second (third? fourth?) the sentiment that baseball hasn't been failing to encourage ethnic diversity.