This may give something to think about for your original question. Median SAT Tiers and US News Rank among national LACs and Universities. Obviously a flawed metric of institutional strength, and there are many extreme outliers like Reed.
2200 or higher: Harvard (2), Yale (3), Princeton (1), Stanford (5), MIT (7), U’Chicago (3), Vanderbilt (15), WashU (19), Caltech (12), Columbia (5), Harvey Mudd (21), Northwestern (12)
Average rank for universities- 8
Only one LAC
2100-2200: Duke (8), Pomona (7), Dartmouth (11), Rice (15), U’Penn (8), Williams (1), Swarthmore (4), Amherst (2), Brown(14), Tufts (27), Claremont McKenna (9), Carnegie Mellon (24), Johns Hopkins (10), Notre Dame (15), Cornell (15), Georgetown (20), Haverford (12), Carleton (7), Vassar (12), Northeastern (39), Bowdoin (6, test optional)
Average rank for universities- 17
Average rank for LACs- 7
2000-2100: Middlebury (4), Wellesley (3), RPI (39), Grinnell (19), Colgate (12), Colby (12), Hamilton (12), Georgia Tech (34), Washington and Lee (11), Reed (87), Rochester (32), USC (23), Emory (20), Cal (20), Michigan (27), Boston College (31), Macalester (24), William and Mary (32), Oberlin (24), Brandeis (34), Scripps (23), Barnard (27), Case Western (37), U of I (44), UVA (24), NYU (36), Davidson (9), Tulane (39), Wesleyan (21, test optional), Smith (12, test optional), Mt. Holyoke (36, test optional)
Average rank for universities- 31
Average rank for LACs- 21
1900-2000: Kenyon (27), Colorado College (24), UCLA (24), St. Johns Annapolis (53), Lehigh (44), University of Richmond (27), UMD (60), Whitman (41), UNC Chapel Hill (30), Villanova (50), Bucknell (32), University of Miami (44), SMU (56), Occidental (44), UCSD (44), Wheaton (77), George Washington (56), USAFA (32), Boston U (39), Rhodes (44), Lafayette (36), UMN (71), USNA (12), UW-Madison (44), Colorado School of Mines (82), New College of Florida (90), UT Austin (56), SUNY Binghamton (86), TU (86), IIT (103), Thomas Aquinas (53), Wake Forest (27, test optional), Bates (27, test optional), Holy Cross (32, test optional), Bryn Mawr (31, test optional), WPI (60, test optional), Pitzer (32, test optional)
Average rank for universities- 55
Average rank for LACs- 37
Here’s another source of data- the mean LSAT of students from particular LACs and universities http://talk.collegeconfidential.com/college-search-selection/1190895-mean-lsat-score-by-undergraduate-college.html The grads at LACs, even those lower ranked like Wheaton, do very well.