Erling Haaland scored his fifth goal in the 58th minute. Not that you would have known it from his celebration, really more of a non-celebration: a desultory jog, a little curl of the lip and a raise of the eyebrow, not so much the expression of a man who has just written his name into the annals of Manchester City history as the look of somebody who has just found a partly melted Freddo in his pocket.

Of course everyone expected Haaland to come off at that point: the game won, Luton’s brief squall of defiance extinguished, passage to the sixth round secure. But he didn’t. The clock ticked past 60 minutes, then 65, then 70. Still not a twitch from Pep Guardiola. You’re 5-2 up. Hang on, Mateo Kovacic has just scored, make that 6-2. You’ve got the derby against Manchester United at the weekend. It’s an open game, tackles and shoves flying in all over the place. Haaland has only recently come back from injury. You have four subs left. So, Pep. What’s the thinking here?

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Naturally the temptation is to diagnose a classic case of Pep anxiety: that elemental need for security and reassurance, the comfort blanket of an extra goal in a wild mood swing of a game, a respect – bordering on dread – for all the ways in which the opposition can hurt you. Six-two, famously, is the most dangerous scoreline of all.

But I’ve got a different theory. I reckon Guardiola was simply as sadistically mesmerised as the rest of us. I reckon he wanted to access one of the few remaining sensations in football that he has yet to experience. He wanted to see Haaland score six.

And of course this is a power flex as much as it is a legitimate tactic: the footballing equivalent of an Australian cricket captain at the Gabba stubbornly running up a colossal third-innings lead and refusing to declare. After all, what’s the point in possessing the most destructive toy in the sport if you’re not going to push it as far as you can? What’s the point in even buying Haaland if you’re not going to let him score six against a far smaller club on a tiny fraction of your wage bill?

As it turned out, Haaland did not score six. Fraud, charlatan, billion‑pound blue bottle job, etcetera. All the same, this was pretty much the consummate exhibition: not just in terms of finishing and movement, the nuts and bolts of forward play, but in the way City are trying to function these days. Gone – for the most part – are the kaleidoscopic triangles and painstaking patterns of the classic Guardiola City sides. The quickest route to goal is the same as it’s always been: a straight line.

This is a more impatient City team these days, a more brutally efficient City team, a more direct and physical City team: a team of bold straight lines and a distaste for ornamentation and small talk. This, perhaps, is why Jack Grealish fell out of favour earlier this season and the hard-running Jérémy Doku was preferred to him. Why the tricky Cole Palmer and Riyad Mahrez were deemed surplus to requirements in the summer and box-to-boxers signed, in Mateo Kovacic and Matheus Nunes. Why City are so much taller these days. Their 2018‑19 title‑winning side was the shortest in the Premier League. These days they are solidly mid‑table, rebuilt and retooled, the height of Haaland and Rodri added.

And perhaps the ultimate expression of this new City directness was their second goal here, a modern twist on route one, Haaland receiving it straight from the goalkeeper Stefan Ortega, laying it back to Kevin De Bruyne and bombing straight on to receive the through-ball. Even the finish was gun-barrel straight, right in between the legs of Tim Krul.

Related: Five-goal Erling Haaland in warning to Manchester City’s rivals

Of course these things are partly defined by the kind of game the opponent makes you play, and Luton’s determination to maintain a high line, to build through the thirds, to leave Haaland one-on-one with Teden Mengi, helped to mould City’s approach.

Bernardo Silva buzzed all over the pitch and Nunes switched from left-wing to right and back again, but in a way this was all distractions and sleight of hand: the mere illusion of sideways movement when Plan A was to go straight down the middle all along.

And, of course, other plans are still available. Not all of City’s opponents will be as unflinchingly obliging as this Luton side. Not all of them will leave themselves so open to the counterattack. City’s reasonably new tactic of holding the ball in deep areas will be less effective against teams who do not allow themselves to be baited into the press. But even in the autumn of the Guardiola era, this is a side is still sharpening and shaping itself into new forms, still exploring its outer limits.

The substitution board finally went up in the 77th minute. Haaland pretended not to see it. Finally he dragged himself reluctantly from the pitch, thinking not so much about the five goals he had already scored but the five days he would have to wait until he could score the next.