Is it bad to enter the NCAA tournament on a long winning streak? Yes.

(updated through 2016 tournament)

In the 32 NCAA tournaments of the six-round era, which began in 1985:

- 16 champions (50%) lost their final pre-tournament game, including the last 3 in a row

- 26 champions (81%) entered with a winning streak of five or fewer games

The only exceptions:

1986 Louisville - won 11 entering tournament, 17 in a row overall

1992 Duke - won 7 entering tournament, 13 overall

1995 UCLA - won 20 entering tournament, 26 overall

1998 Kentucky - won 7 entering tournament, 13 overall

2008 Kansas - won 7 entering tournament, 13 overall

2013 Louisville - won 10 entering tournament, 16 overall

The longest single-season winning streak to fall during a tournament?

2015 Kentucky - 38 in a row

In the earlier years of the NCAA tournament (pre-1985), an era of significantly less parity, long winning streaks were much more common among champions:

1941 Wisconsin - won 14 in a row to end the season

1943 Wyoming - won 29 in a row to end the season

1948 Kentucky - won 16 in a row to end the season

1955 San Francisco - won 25 in a row to end the season

1956 San Francisco - went undefeated, 29-0 (so this was a 54-game streak overall)

1957 UNC - went undefeated, 32-0

1961 Cincinnati - won 22 in a row to end the season

1962 Cincinnati - won 18 in a row to end the season

1964 UCLA - went undefeated, 30-0

1965 UCLA - won 15 in a row to end the season

1967 UCLA - went undefeated, 30-0 (so this was a 45-game streak overall)

1968 UCLA - won 16 in a row to end the season

1971 UCLA - won 15 in a row to end the season

1972 UCLA - went undefeated, 30-0 (so this was a 45-game streak overall)

1973 UCLA  - went undefeated, 30-0 (so this was a 75-game streak overall)

1974 NC State - won 28 in a row to end the season

1976 IU - went undefeated, 32-0

1978 UK - won 13 in a row to end the season

1982 UNC - won 16 in a row to end the season

1984 Georgetown - won 12 in a row to end the season


So the answer to the question posed in the post title would, statistically, be yes.  It's been rare for teams to keep momentum all the way through March and April, especially since the tournament expanded to six rounds.

Most impressive regular season run at the top since...?

Being #1 obviously puts a target on your back, and this UK team has withstood the pressure unlike many in recent seasons.  This week, UK will remain #1 for the 7th consecutive AP poll.

Over the last few years, a number of teams have put together equal or better streaks:
2005-06 Duke = preseason #1, plus 10 additional weeks
2007-08 UNC = preseason #1, plus 10 additional weeks
2008-09 UNC = preseason #1, plus 7 additional weeks
2009-10 KU = preseason #1, plus 8 additional weeks
2010-11 Duke = preseason #1, plus 9 additional weeks

The obvious caveat here: all of the above streaks began at the season's outset, when it's arguably easier to retain the #1 ranking against an often-shoddy non-conference schedule.  Sure you might be tested in an early-season tournament or in-state rivalry game, but you won't be challenged as consistently as you are during the conference schedule.

Therefore, I think you have to go back to 2004-05 to find a run at the top more striking than this Kentucky team.  That year's Illinois team stayed at #1 for a remarkable 15 weeks through the heart of the season, before going on to lose in the national title game.