Do we really, though? Bautista, EE, Donaldson and Tulo all hit at a significantly above-average level against both RHP and LHP (Tulo is the worst against RHP, with a career 115 wRC+ against them).
Meanwhile, Heyward and Davis are both below league average in their careers against LHP, showing significant splits as most lefty hitters do (I'm assuming this out of intuition).
You can put a LOOGY in an important spot against Davis and suddenly the latter is not as effective/dangerous (still has tremendous power obviously), but you put a right-handed reliever against any of JB, JD, EE or Tulo and they're all still elite hitters, as we saw many times this year. Brett Cecil against Chris Davis wasn't even fair.