It's too difficult for a lefty 2B, SS, and 3B to make the throw over to first base. They have to turn their entire body and won't get as much on the throw as a righty would.
There have actually been quite a few lefty infielders, mostly about 100 years ago.
2B - Total of 57
Bill Greenwood (538 games), Bill McClellan (436), Tom Evers (110), Lip Pike (79), Bob Addy (79), Roger Connor (68), Sam Trott (65), George Decker (40), Al Reach (36), Hal Chaase (35), Jimmy Hallinan (25), plus 46 more. Last one was Don Mattingly during the completion of the Pine Tar game in 1983.
SS - Total of 43
Jimmy Macullar (325), Bill McClellan (246), Jimmy Hallinan (111), Billy Hulen (92), George Van Haltren (79), Billy Redmon (61), Jimmy Ryan (58), Jack Leary (40), Russ Hall (36), Sy Sutcliffe (31), Bill Greenwood (30), Lefty Marr (29), plus 31 others. Last one was Lou Gehrig in 1934 who actually didn't play shortstop. He was listed at shortstop to keep his consecutive game streak alive. He batted in the top of the first, got a single and was removed for a pinch runner. Before him the last was Hal Chase in 1909.
3B - Total of 52
Hick Carpenter (1059), Lefty Marr (129), Roger Connor (111), Bill McClellan (58), Chris James (48), Willie Keeler (44), Spud Johnson (44), Jack Leary (37) plus 44 others. Last was Mario Valdez in 1997.
C - Total of 29
Jack Clements (1073), Sam Trott (272), Pop Tate (202), Sy Sutcliffe (186), Fergy Malone (178), Bill Harbidge (159), Mike Hines (99), John Humphries (75), Fred Tenney (71), Art Twineham (52), Phil Baker (50), Jiggs Donahue (45), Dave Oldfield (35), Charlie Housholder (34) plus 15 others. Last one was Benny Distefano in 1989.