The Spurs were awful for one season because David Robinson missed almost the entire season, Sean Elliott missed half the season, sixth man Chuck Person missed the entire season, and other injuries. The Celtics of this season weren't half as wrecked as the 96-87 Spurs were. That's a fluke loss of talent due to injury that you can't plan to copy.
The Bulls were lucky and got Derrick Rose when they had only the ninth-worst record and only a 1.7% of winning the lottery. You can't plan on getting that lucky.
The Magic seemed to collapse because their defense deserted them, but it isn't obvious from the stats as to why. I can't immediately explain why they did so bad without doing some research. Still, they weren't a playoff team until Dwight Howard's fourth season and they didn't get to 55 wins until his sixth season.
The Celtics got to that 5th pick due to Paul Pierce's injury and some really egregious tanking (they were 20-27 with Pierce, 4-21 without him). And they traded the pick rather than using it to draft a possible franchise player.
#1 overall picks since 1980 who have been on a world championship team: Mark Aguirre (twice), James Worthy (thrice), Hakeen Olajuwon (twice), David Robinson (twice), Shaquille O'Neal (four times), Glenn Robinson (once), Tim Duncan (four times). Worthy and Duncan are the only players on that list to get a ring in their first seven seasons. If we exclude the last seven drafts, then 28% of first overall picks since 1980 have won an NBA title.
If you wanted a team like Boston to tank and be bad in order to get a top draft pick, it probably involves a 2-3 year slide towards the bottom without drafting any starter-caliber players, followed by 4-5 years of surrounding a superstar (if you get one) with talent, longer if you fail to draft a franchise player in your first crack at it.