Let's take the last 15 years (2003 - 2017) and try to figure out how a double elimination tournament would have shaken out.
First, a list of the #1 seeds and the eventual champion, just to set the stage.
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To make this a bit easier, let's say that every time a 1 seed won the title eventually, they would still win, so the champions from 2005, 2007, 2008, 2009, 2010, 2012, 2013*, 2015, and 2017 all stay the same.
So let's look at the other years:
2003 - Syracuse
2004 - UConn
2006 - Florida
2011 - UConn
2014 - UConn
2016 - Villanova
In 2003, the best three teams in the country were Arizona, Kentucky and Texas. Arizona had Jason Gardner (All American), plus three future NBA players in Andre Iguodala, Luke Walton and Channing Frye, and another stud in Salim Stoudemire. That team was loaded. KU took them down in the regional final, but I don't know that KU can get them twice because Arizona may well have been the best team in the country. Either that, or Kentucky was. UK had more of a great college team with Chuck Hayes and Keith Bogans leading the way, but they were very good. Texas had TJ Ford (player of the year), plus Brian Boddicker and Royal Ivey (future NBA player). If it's me, I say Arizona wins a double elimination tournament. They were just so talented. If they get another crack at KU (we beat them by just three), I don't know that we get it done.
2004, UConn was a very good team (2 seed). St. Joseph's and Stanford both went through most of the season undefeated, but the best team was almost certainly Duke. JJ Redick, Luol Deng, Daniel Ewing, and Chris Duhon formed an elite collegiate perimeter attack, with Sheldon Williams in the middle. Duke blew a 7 point lead in the national semifinal against UConn and lost by one. Given a second chance, it's likely Duke lifts the trophy.
2006, we know now that the eventual champion Gators were loaded, but we didn't know it at the time. However, the scariest team was probably either UConn or Duke. Duke lost to LSU. UConn lost to George Mason. Duke had the transcendent JJ Redick year (he averaged over 26 points a game) along with Sheldon Williams (almost 19 from him). UConn was lead by Rudy Gay. No way George Mason beats them twice. The title game is probably Duke - UConn in double elimination format. Flip a coin on who wins that one.
2011, the best team was KU, trailed by Ohio State. KU had the Morris twins, Tyshawn Taylor, and TRob. Ohio State was led by Jared Sullinger. There's a reason both of these teams were in the Final Four the very next season. If things are double elimination, KU and Ohio State play for the title in 2011, rather than the national semifinal in 2012, with KU likely winning that game as well.
2014, the best team was Arizona. Aaron Gordon, TJ McConnell, Rondae Hollis-Jefferson, etc. They got edged by a very good Wisconsin team in the regional final, but I don't know that anybody could have beaten them again. They were so, so talented. Florida had a nice team that might have snuck in if Arizona stumbled. That Wisconsin squad was also good enough to make noise, but ultimately, Arizona is the likely champ.
2016, the best teams were Kansas and North Carolina. North Carolina very nearly won the title anyway, so we know what they could have done. KU lost the regional final, but had a stacked team with Ellis, Selden, Mason, etc. UNC is probably better, but I don't know if Roy Williams could have gotten focused for a title matchup with KU. Flip a coin on this one.
So the final title breakdown would be as follows:
2003 - Arizona, or maybe Kentucky
2004 - Duke, or possibly UConn or Stanford
2006 - Duke or UConn
2011 - Kansas, maybe Ohio State
2014 - Arizona, maybe Florida or Wisconsin
2016 - North Carolina or Kansas
Duke probably adds two titles to the five they already have (doesn't cost them any titles). Arizona might have two more. KU adds at least one.
However, since I didn't look at any of the years where a 1 seed did win, there's no guarantee that a different top seed doesn't win the title. Illinois was great in 2005. Ohio State and UNC were both tremendous UNC was pretty stacked in 2008, as was Memphis. UConn had a great squad in 2009. Kentucky probably had the best team in both 2010 and 2015. KU might have had a shot in 2013 or 2017.
On the other hand, maybe KU can beat Arizona twice, and they could knock off Syracuse in a second meeting. Maybe Florida does make that run in 2006 (they had the talent). Kentucky has had some talented squads the last several years. Double elimination probably gives Calipari three or four titles instead of just one.