The problem is that their consistency lately hasn't been because they're that good, it's because the NVL is straight up terrible. If they were doing this in even a decent league like the SWC or CCC it'd be different.
While I agree the NVL has become a terrible league, it's hard to question the consistency of a program that has been to seven straight state championship games and nine in the last ten years. Judging them against their NVL foes is silly. Ansonia hasn't lost a league game since Thanksgiving 2010. You really have to judge them independently, which is hard to do. Since you mentioned the SWC and CCC, Ansonia has faced teams from both leagues (usually in the playoffs) and faired rather well. So, I don't think judging them against those leagues is fair either because they've beat them far more then they've lost. The only real way to judge how good they are is in the playoffs against the "top" teams from other leagues. Historically, they've been pretty good in those games.
Year Result Game
2016 Ansonia 28 Rocky Hill 21 Class S Final
2016 Ansonia 49 Cromwell/Portland 28 Class S Semifinal
2016 Ansonia 48 Stafford/Somers/East Windsor 0 Class S Quarterfinal
2015 Bloomfield 31, Ansonia 20 Class S Final
2015 Ansonia 31 Trinity Catholic 22 Class S Semifinal
2015 Ansonia 35 Capital Prep 13 Class S Quarterfinal
2014 Valley Regional 21 Ansonia 20 Class S - Small Final
2014 Ansonia 35 Windham 14 Class S-Small Semifinal
2013 Ansonia 51 Woodland 12 Class S Final
2013 Ansonia 49 Rocky Hill 27 Class S Semifinal
2013 Ansonia 49 Coginchaug Regional 21 Class S Quarterfinal
2012 Ansonia 59 North Branford 26 Class S Final
2012 Ansonia 41 Hyde 13 Class S Semifinal
2012 Ansonia 53 Prince Tech 16 Class S Quarterfinal
2011 Ansonia 38 Ledyard 0 Class M Championship
2011 Ansonia 48 Berlin 14 Class M Semifinal
2011 Ansonia 35 Bethel 6 Class M Quarterfinal
2010 St. Joseph 49 Ansonia 28 Class S Runner-up
2010 Ansonia 46 Montville 15 Class S Semifinal
2010 Ansonia 47 Hyde 26 Class S Quarterfinal
2009 NW Catholic 24 Ansonia 0 Class S Semifinal
2008 Cromwell 14 Ansonia 12 Class S Runner-up
2008 Ansonia 28 North Branford 0 Class S Semifinal
2007 Ansonia 35 New London 0 Class S Championship
2007 Ansonia 25 NW Catholic 7 Class S Semifinal
2006 Ansonia 34 Bloomfield 14 Class S Championship
2006 Ansonia 47 North Branford 14 Class S Semifinal
2004 Cromwell 27 Ansonia 19 Class S Playoff
2003 Ansonia 55 Cromwell 0 Class S Championship
2003 Ansonia 67 Hyde 14 Class S Playoff
2002 Ansonia 44 ND Fairfield 14 Class S Championship
2002 Ansonia 39 Immaculate 7 Class S Playoff
2001 North Branford 21 Ansonia 20 Class S Playoff
2000 Griswold 7 Ansonia 6 Class S Playoff
1999 Bloomfield 56 Ansonia 0 Class S Runner-up
1999 Ansonia 35 Tolland 22 Class S Playoff
1998 Bloomfield 40 Ansonia 7 Class S Runner-up
1998 Ansonia 45 Putnam 21 Class S Playoff
1997 Darien 23 Ansonia 6 Class S Playoff
1996 Darien 31 Ansonia 20 Class S Playoff
1995 Ansonia 7 Bloomfield 0 Class S Championship
1995 Ansonia 16 Sheehan 6 Class S Playoff
1994 Ansonia 54 Bloomfield 14 Class SS Championship
1992 New London 21 Ansonia 19 Class S Runner-up
1991 New London 34 Ansonia 18 Class S Runner-up
1989 Ansonia 44 Weston 0 Class S Championship
1988 Ansonia 20 New London 15 Class S Championship
1987 Ansonia 28 New London 27 Class S Championship
1984 Ansonia 56 Putnam 6 Class S Championship
1983 Ansonia 32 Stamford Catholic 0 Class S Championship
1982 Ansonia 14 Derby 0 Class S Championship
1981 Ansonia 23 Wilson 6 Class SII Championship
1980 Newington 24 Ansonia 14 Class L Runner-up
1979 Ansonia 28 Seymour 14 Class M Championship
1978 Amity 35 Ansonia 22 Class L Runner-up
1977 Ansonia 20 Stamford Catholic 7 Class S Championship
1976 Ansonia 6 Derby 0 Class S Championship
Title Games: 20-10
Overall Playoffs: 41-16