McKenzie, still one of the Australian greats, began his test career as a 19-year-old in 1961, took five wickets on debut to win a test against England at Lord's and went on to take 246 wickets over 60 tests at a highly respectable average of 29.
The key comparison with Cummins is that both had easy actions, could get swing and seam, and hit the pitch and bat with a very hard ball. Cummins gets bounce, bowls routinely at 145km/h and has a nasty faster ball that breaks the magic 150km/h mark with some ease.
Most are picking the McKenzie route for Cummins, though that will likely depend on how well the Australians marshall this new resource.
Young fast bowlers who are overworked tend to find injury an unwelcome but persistent visitor - and Australia have virtually non-stop international cricket until the end of the West Indies tour in April.
Captain Michael Clarke has already called for a rotation programme to safeguard this new fast bowling asset.
Cummins bowled 44 overs in the second test against South Africa and the dangers of over-use are better seen when it is realised his state side bowled him for 48 overs in the first innings and 65 in the whole match in the Sheffield Shield final this year.
Like McKenzie at a young age, Cummins has already surprised observers with his poise and maturity for one so young. He apparently wears a continuous smile - until he takes the pitch, when the fast bowler persona takes over - and is not just a snorter and a blaster.
In the recent two-test series against South Africa, where he won the man of the match in the second test, Cummins sorted out no less a presence than Jacques Kallis - the tough South African all-rounder who has seen it all and is one of the few men to have surpassed 12,000 test runs; he sits fourth in the all-time test run scorers table (with only Ricky Ponting, Rahul Dravid and the great Sachin Tendulkar ahead of him).
Kallis got several nasty short balls before nibbling at one outside the off stump and was caught at slip.
"Yeah, he's obviously someone who has been a stalwart of the game. He's been an unbelievable player for South Africa," Cummins told the Australian. "The plan was to give him a couple of short balls and if we could tie him up a bit outside off stump, he might fish at one. Fortunately that worked."
If he blasted Kallis out in time-honoured fast bowler style, Cummins showed maturity beyond his years when he cut down on his pace to seek swing in morning conditions that favoured that movement.
"I guess if speed comes at the price of losing accuracy, I don't think I'd want to bowl extra pace," he said.
"In four-day and five-day cricket, it's harder to maintain the speeds all day. If you're in a spell with someone down the other end who is keeping it tight, you might have the ability to try and rip in and try and start intimidating the batting."
For all that, he seems to have a fast bowler's soul: "Scaring them is enough," he told the Sydney Morning Herald. "It's really exciting, seeing the fear in the batsman's eyes. I love trying to bowl fast."
Cummins does not know if he can bowl faster but is curious to see what happens with "a bit of wind behind me ...". His primal joy is as strong as ever.
"I think when a batsman can look up at the scoreboard and see the radar ticking over 150, it doesn't even matter where you're bowling."
