They had some pretty high picks for a 6 year run between 2013 & 2018 though:
5 OV
7 OV
5 OV
13 OV
12 OV
2 OV
2010: 7th oa, Jeff Skinner, was the best player through the dark years but moved after Brind'amour took over the team over concerns that he wasn't a good enough two way player. The 2nd in that trade became Pyotr Kotchetkov
2011: 12th oa Ryan Murphy, bust
2012: 7th OA, traded for Jordan Staal (who would win the playoff MVP 14 years later)
2013: 5th oa Elias Lindholm, traded with Noah Hanifin for Dougie Hamilton (walked after 3 years), Michael Ferland (walked after 1 year) and Adam Fox (demanded to be traded to Rangers, supposedly he lied to Don Waddell about a willingness to sign in Raleigh?), developed into a decent top 6er that some teams deemed better than he actually was. Also it was a running joke for a while on the Canes board because one poster was mad that Jim Rutherford didn't try harder to move up one spot and take Seth Jones and refused to let this go for YEARS, like all Rutherford had to do was call Nashville and throw in a 3rd in 2017 to get them to swap lmao
2014: 7th oa Hadyn Fleury, taken by Ron Francis in expansion draft, 3rd pairing defenseman
2015: 5th oa Noah Hanifin, see Lindholm's entry, developed into a top 4 minute muncher but didn't become a #1 franchise defenseman as hoped. Also got wrecked by the Blake/Stankoven/Hall unit in the finals, so that was nice
2016: 13th oa Jake Bean, traded to the Jackets for a 2nd round pick, 3rd pairing defenseman. Also taken 1 spot ahead of Charlie McAvoy
2017: 12th Martin Necas, middle 6 winger in Carolina, top line winger in Colorado, easily the 2nd most impactful player on this list for the Canes and in terms of contributing to the Cup win, he was traded for Rantanen, who was then moved for Stankoven + 2 1sts, one of which would be part of getting K'Andre Miller
2018: Svechnikov, 2nd oa, lottery win gets Carolina a top line wing skilled/physical winger
Point is Canes won a Cup despite squandering over half a decades worth of high picks that mostly didn't contribute to the Cup win. High picks clearly matter so it's interesting how the team's construction is somehat against the grain, like they still got Svechnikov, but Svechnikov isn't a Barkov, or Stamkos/Hedman, or a MacKinnon/Makar