Yes, it's counterintuitive, but remember, while the Spurs would get the #1 pick and get Davis, the #2 team might be really smart and take Otto Porter who's arguably the better player to Davis bc he plays perfect basketball every minute he's in the game. The teams records show a lot of that.
The teams picking lower would have to innovate, either by mastering draft or even better proving the draft isn't as important as everyone thinks. Who wouldn't have drafted Wilt Chamberlain over Bill Russell, yet Russell is the greatest basketball player to ever live?
Plus, "make it take-it draft" would have fans going bezerk rooting for each and every game no matter how insignificant, and fandom would go thru the roof bc everyone (even if they don't like to admit it) loves a dynasty. People who hate the dynasty watch more of the sport that people who like the dynasty. Plus, the dynasty would be like an all-star game, every game they play. Like watching 1980 Olympic Hockey, people would have their eyes glued to the TV waiting to see if American amatuers can topple the great Russian hockey machine.
Draymond ALWAYS moves the needle. The Hornets could've picked up TJ McConnell as starting PG. At center would be Hassan Whiteside. At small forward Robert Covington. Shooting Guard? There's a million good ones, all sitting bench hoping for minutes. Crabbe, Stauskas, Denzel Valentine, Bogdan Bogdan-- they are all probably easily attained. The Larry Brown Pistons proved you don't need superstar draft picks to win the title, they almost won it back to back.
There's a MASSIVE groupthink going on right now that you have to have a LeBron or a Curry or a Dirk to win a championship. All those players had legit TEAMS around them. The GSW won their first championship (and should've won their 2nd in a row) without Durant. Curry and Klay were underdog picks, not top 2, and Draymond as you pointed out was 2nd round.
If you're gonna finish 30th every year, then sure, you're team's going to stink and probably gets moved to a new city, new owner. Good riddance.
Also, you're talking about something that's still impossible in today's league, going 30th to 1st. You don't have to move from 30th to first, you need to move from 30th to 25th to 20th the 15th to 10th to 5th to 1st. Ever play that card game called "asshole"? The asshole never rises up and becomes president the next hand, he has to work his way out of the jam, but assholes rise to be presidents over and over again in that game.
The draft is mostly nonsense anyway, the draft sometimes makes the player. Anthony Bennett stayed in the league probably an extra 4 years simply bc he went #1, yet Quinn Cook is ripping up D-League and can't get a 15th man seat at the table. TJ McConnell is an ideal PG yet he'd never have cracked the league except for Philly having no butts to fill seats for 2 years so they took chances on him and Covington.
So yeah, the system would totally work, you'd never have to worry about tanking again, every game would be fought hard, there'd be no DNP rests, no tanking, no respect for losers whatsoever. You wanna win? then as Bill Parcells would say "find a way to win".
Not a single person in the entire league would rather have Otto Porter than Anthony Davis. That's just absolutely ridiculous.
Let's take your example of moving from 30th to 25th to 20th etc. Let's say we start in 2012. This is the team that you would get with that style of draft:
2012: Festus Ezeli
2013: Reggie Bullock
2014: Bruno Caboclo
2015: Kelly Oubre Jr.
2016: Thon Maker
2017: De'Aaron Fox
There's a zero percent chance that team isn't just straight awful.
What you're suggesting just simply isn't possible nor practical. Even if a team keeps finishing last and the team moves owners and cities, the team is still behind the eight-ball and there's no way they could dig themselves out of that hole.
You mention that teams don't need a superstar to win a championship, but let me tell you this stat: Only one team in the history of the NBA has won an NBA championship without a Hall of Famer (or surefire future hall of famer ie Duncan, LeBron, Dirk). That team was the 2004 Pistons who had a Hall of Fame coach. There's no argument for that.