The old league teams took pride in retaining the ball for huge swathes of time, just as in Super Rugby a graphic pops up on the screen noting for approval that 16, 17, 18, and more phases have clocked up.
The 1960s league games played at Carlaw Park, which was fondly referred to as The Swamp, saw two lines of massive, tough, and often very skilled men line up across the field and smash into each other. Rugby players like Brodie Retallick, Ardie Savea, and Sam Whitelock would recognise the situation in a flash.
So it's hardly a surprise that Tuivasa-Sheck has adjusted so quickly to the broken-field play which is now such an integral part of rugby. After all, his spatial awareness has been sharpened in the most intense league competition in the world.
It's slightly odd that more New Zealand league players haven't come home to take a shot at rugby.
Cash isn't really an issue. A rugby career that builds from an All Black start to European club rugby is often financially ahead of the NRL. It was reported in the Sydney Morning Herald that, before Covid-19, Daly Cherry-Evans topped the NRL rich list at $1.35 million a season.
Great money indeed, but former All Black Charles Piutau is on $2.05 million a year at Bristol in England.
Then there's the issue of home comforts. Sydney and Brisbane may feel like home, compared to living through English winters, or struggling to learn a new language in France. But Auckland is home for Tuivasa-Sheck, and with the Blues humming it must feel pretty welcoming.
Not every league-to-rugby switch has been hugely successful. Before the 2015 World Cup there was the brain explosion from England's coach Stuart Lancaster, who rushed league star Sam Burgess into the centres in his Cup team.
Burgess had been a fearsome prop in the NRL, and given time he would have almost certainly developed into a very good rugby flanker. But he wasn't a test-quality midfielder.
On the other hand, when the All Blacks won the Cup at home in 2011, they had two terrific former league players on board, Brad Thorn and Sonny Bill Williams.
Both New Zealand-born, they had to face prejudice when they switched codes and came back from Australia.
Thorn returned to New Zealand in 2001 for a shot at being an All Black lock. He was selected that year to tour with the All Blacks, but turned down the jersey because he wasn't sure his future lay with rugby.
On radio he was castigated as a mercenary, using rugby to pump up his value as a league player, but Crusaders teammates know it was bedrock integrity. Once he was ready for the All Blacks in 2003 his coaches loved him.
"He's easy to coach," said Steve Hansen. "Just give him something to push, give him something to tackle, give him something to catch, and he's happy. And give him three feeds a day. Just make sure they're big ones."
In most rugby test teams in the world Williams would have been a first-choice No 12. It was his misfortune that the best second five-eighth in All Blacks history, Ma'a Nonu, had a lock on the No 12 jersey.
Williams copped it from grumpy old-school guys who seemed to resent the way he excited young fans. In reality he was a huge talent, and it was hardly his fault that when he had to change a torn jersey on the pitch a video of his ripped torso attracted more hits on YouTube than any action from the game.
Finally, if there was more movement from league to rugby, should there then be sympathy for the NRL?
Maybe not. In amateur rugby days the Wallabies were often decimated by league signings. A prime example of a rugby gift to league? The little guy in the Provan-Summons Trophy for winning the NRL premiership is Arthur Summons. His Western Suburbs team had just lost the 1963 grand final to Norman Provan's St George when the famous image of the mud-coated gladiators was snapped. For four years before he signed to play league in 1960 he'd been the Wallabies' first five-eighth.