I'm deliberately putting my response to the second part to avoid a wall-o-text since it is more historically fastidious:
Is there some reason you're forgetting that Anthony Davis exists? I thought you were restricting yourself to "Rising Star" centers or thereabouts, but you keep talking about Cousins, so that hardly makes sense.
Make it 42 years to cover the modern era. First, you're wrong. We're talking classic bigs, not just centers, so guys like Tim Duncan needs to be added to that list. Okay, let's dig in.
I see Anthony Davis and Tim Duncan more as power forwards and part time centers. But ok, include Anthony Davis as it strengthens my argument.
Since we went back to the ABA-NBA merger, our first championship is headed by PF/C Bill Walton's Trailblazers. The very next year? 6'9" PF/C Elvin Haryes and his Bullets. Who unseated them in the Finals the following year? Center Jack Sikma's Sonics. See a pattern?
Hayes was a power forward and Sikma was not a dominate center and was part of a well balanced team.
Meanwhile, while they needed guards, if you look at these "small" guys who disrupted this, and dominated as alphas in the 80's, that would be the 6'9" Magic/Larry, and they always had league-dominating classic bigs as their main sidekicks (Old-KAJ/Parrish/McHale). KAJ was still in full alpha mode when 1980 took off, the year after Sikma's crown, with rookie Magic aboard, to collect their first ring together. In Magic's case, he depended on this "sidekick", the greatest center in history, to produce the majority of his team's scoring up until 1986-87. Thought a Kobe nuthugger might find that interesting.
Who is calling KAJ a sidekick? Mchale is not a center and Parish, although a great player and integral piece, didn't lead the team and could have never led a team to a title.
The Bad Boys were a team dynamic. Thomas was the Captain, no doubt, but Laimbeer was a defensive specialist and enforcer who both scored and rebounded better than Gobert, for example, while Rodman was the greatest rebounder in history. Still, we'll give that to smalls: Thomas/Dumars.
You're spending a lot of time talking about forwards and role players.
That brings us to the 90's which outside of Jordan were dominated by classic big men: Olajuwon & Robinson (Ewing/Shaq were Jordan's punching bags). Jordan was the earthquake who inspired all this to change. He was the only guard-- Chicago the only dynasty-- in modern NBA history prior to the rise of Downtown Moneyball that didn't need a truly great big man to reign.
There has only been 3 dynasties since the 80s lol. One was led by a SG, another by a C/SG combo, and the other by a PF/great team/great coach/great organization combo.
Nevertheless, Shaq & Duncan succeeded him in owning the league. During their reign, Detroit squeezed in another defense-centered team concept championship, but this time with their defensive MVP being their center, in Ben Wallace, not a guard like Dumars, and he was as small as classic big men come. Miami also squeezed in an outlier behind Wade-- perhaps the only guy besides Jordan to do it without a great big even if only once.
Ben Wallace was a utility player tho...he's not leading you to a title. Detroit was another well balanced team.
Boston got theirs, but while most perceive Paul Pierce as the leader of that team, Garnett was easily the greater player, and unsurprisingly the one who produced both more Win Shares and a higher VORP in their championship season. Pierce got all the attention because he was a crunchtime scorer.
Finally we arrive at alpha Kobe, but Kobe needed Hall-of-Fame lock Pau Gasol to win his back-to-backs. That was the end of the dominant big man.
Garnett and Gasol are again, power forwards. When going over the history of centers who won titles you have mentioned and included 7 power forwards and several role players/supporting cast members.
So I repeat my original assertion. In the past 40 yrs only 4 centers have led, or co-led, their teams to titles(5 if you include Unseld which is fair). And only 3 have led their teams to multiple titles.
Last decade saw a fading Oneal, Ming, Howard, Gasol(prior to his Laker years), Ben Wallace as the premier big men. All quality players but we have bigger pool of quality centers in this era. The 4 dominate centers of this era(Towns, Embiid, Cousins, Davis*) have the skill sets and potential to put up numbers and lead teams to titles. Haven't been this many since the 90s.
