Let's take a look at really good teams in recent years, and ask how they were constructed:
Golden State -- Curry 7th, Klay 11th, Barnes 7th, Bogut trade, Draymond 2nd round, Iggy FA
Atlanta -- Horford 3rd, Millsap FA, Teague 19th, Korver FA, Carroll FA
Houston -- Harden trade, Dwight FA; previously Yao 1st, McGrady trade
LAC -- Paul trade (included high draft assets Gordon and Aminu), Griffin 1st, Jordan 35th
Memphis -- Gasol trade / 2nd round, Z-Bo trade, Conley 4th
San Antonio -- Duncan 1st, Kawhi trade-to-draft, Parker 28th, Ginobili late 2nd
Cleveland -- LeBron 1st / later FA, Kyrie 1st, Love trade (included 1st), previously Varejao 30th, Mo Williams trade, Big Z 20th, Boozer 35th
OKC - Durant 2nd, Westbrook 4th, Harden 4th, Ibaka 24th
Indiana - George 10th, Hibbert 17th, West FA, Hill trade, Stephenson 40th
Miami - Wade 4th, LeBron FA, Bosh FA, previously Shaq FA, Haslem Undrafted FA
Portland - Aldridge 2nd, Lillard 6th, previously Roy 6th
Denver - Melo, Nene (draft-trade), Billups (trade), JR Smith (trade)
New York - Melo trade, Chandler FA, Stoudemire FA
Chicago - Rose 1st, Noah 9th, Boozer FA
LAL - Kobe 13, Bynum 10, Pau trade, Odom trade, earlier Shaq FA
Dallas - Dirk 9th, Terry trade, Marion FA, Chandler trade, Kidd trade
Boston - Pierce 10th, KG trade, Allen trade (involved 5th pick), Rondo 21st
Orlando - Dwight 1st, Rashard FA, Hedo FA, Nelson draft-trade
Phoenix - Nash FA, Stoudemire 9th, Marion 9th
Utah - Deron 3rd, Boozer FA
I've bolded the teams that look like they didn't rely on high draft picks.
Even among those exceptions, picks in the later part of the lottery were used. Some of the "trades" involved top 10 picks, e.g. Danilo Gallinari for Melo. We just saw this year how hard it can be to trade up even into that range.