They didn't really. They were just bad when they drafted JJJ. It would've been like had DeRozan gotten hurt this year. They only tanked in 2019, and that really only involved trading Gasol. Most of the other pieces they "let go for nothing" (Conley was traded, but that was because they drafted his replacement, not so the team would lose a bunch of games). What they never did was have a 76ers-style rebuild. The bigger point though is that before they tanked, they didn't tank, and waiting wasn't an issue for them. The Spurs tanking now or in three years means nothing to their long-term prospects. I'd much rather watch them fight for the playoffs than not, so as a fan, I don't see tanking as a good option.
To your second line, the way to build a contender is three-fold. First is you draft a star. Then you sign a star. Finally you trade for a star. Note: Step one wasn't to draft a franchise player. Tanking and trying for the top pick year after year is unnecessary. Developing a top 25-40 player is fine. Then you sign a guy. That's almost certainly going to mean having a flexible cap situation and a decent roster of young/cheap players. This is obviously where you'd want to get the contender's best player, but that's hard for a lot of reasons. A max contract and good situation should still be enough to sway guys in the 10-20 range though, like the Spurs signing Aldridge. Finally, you parlay that young, cheap core into a final star. That trade is hopefully just for a finisher in the 15-30 range, but more and more it's looking like that's where the stars come from. Be prepared to throw away seven firsts and every decent young player in order to get that core together.
Does that seem hard? It might be, but it's simple and straight-forward. It's way easier to do that than to draft a young core in a short window and basically be a le contender before the contracts get too big. That's basically impossible. People mistake being an "up-and-coming" young club with talent with being an actual contender/winner. They're very different things. Few non-contenders are truly close to a le. Most good non-winners have a glass ceiling above them.