Being a 2 way player above HS, whether college or Milb is incredibly tough, if a player is going to be at the top echelon for both.
In my view, the "game" transitions who pitches rather than the player. Sometimes the "game" is the MLB club which drafts the player. Locally we have had a couple of 2 way HS players drafted very high. Word was the MLB team would let them do both.
That lasted less than one week and pitcher only was the result.
In terms of others above HS, I would propose the game itself ends up as the distinguishing factor in more situations than not. Hitting in college is not like hitting in A ball. Hitting in A ball is not like hitting in AA ball. Having an elite type arm provides a back up but the inability to adjust each step of the way and be successful as a hitter is at least as important in the criterion in my view. I just don't think many players get the choice to make above HS. Either their coaches or their organization, or their inability to adjust as a hitter makes it for most.