What exactly is the purpose of a left handed batter. Yes, they're supposed to hit right handed batters, REALLY well but right handed batters hit right handed pitchers really well because that's most of what they've faced their entire baseball lives because most pitchers are right handed.
Right handed batters hit very well against left handed pitchers but, as a rule, left handed batter hit left handed pitchers really badly. Is the difference between most right bat - right pitch and left bat - right pitch so great that you'd want so many left handed batters on your roster, ever?
I've never built a major league roster but I'd think you'd want, at most, two left handed batters plus one switch hitter, nothing like this team currently has. You should be able build a lineup with all right handed batters to face both left and right handed pitchers.