To understand the excitement of Draft Picks, you have to consider two major facts:
1st: When you draft a player, he is under your control for 8 years(and he is guaranteed to not earn to much money for 4 years), which is very attractive, especially to the not prime FA franchises
2nd: Draft Picks are the NBA´s main currency. You can think about it, as Draft Picks in the NBA basicly serve the same purpose as money does in the economy. It is the currency that helps participants of the market, to exchange goods(players in this case). Having a lot of Draft Picks equals, having a lot of money, which is obviously a good thing.
I am not judging the value of having draft picks and tanking vs having "better" players and beeing competetive and so on. Just trying to explain.