The list of the greatest unbeaten single-figure innings in Test history is not a prestigious one, but its members all share cult-hero status. In no other sport are players so prominently exposed for their inability in one facet of the game - Neymar wouldn't make much of a centre-back, but he doesn't ever have to spend 30 minutes trying to rescue a point there - and while those who fail are mocked, success as a tailender can turn an unremarkable player into a legend.
Leach's 60-minute, 17-ball epic in a remarkable last-wicket stand of 76 with Ben Stokes to haul England across the line at Headingley could so easily have been forgotten. Stokes offered a difficult catch to Marcus Harris at third man, repeatedly cleared fielders on the rope by the finest of margins, and would have been lbw but for the absence of DRS; if any of those had turned out differently, Leach's efforts would have been an irrelevance.
Instead, he found himself exalted.
"I don't know what it is," he said. "It's probably because I look like a village cricketer out there in my glasses, the bald head - maybe people think 'that could be me!' All the others look pretty professional.
"The support's been amazing, the support today for all of us was incredible. The noise was insane, and I'm just enjoying playing for England."
While wiping his glasses before facing each ball made him a subject of amusement, Somerset's former strength and conditioning coach Daz Veness paid tribute to his "outstanding mental strength".
"Bat down, gloves off, helmet off, glasses off, glasses cleaned, everything back on in reverse order," he tweeted. "You'll bowl when I'm ready and my mate has caught his breath. And not before."
Bat down— Darren Veness (@DazVeness) August 25, 2019
Everything back on in reverse order
You'll bowl when I'm ready and my mate has caught his breath. And not before.
Outstanding mental strength from The Nut
In the manner that county team-mate Marcus Trescothick has done in the final years of his career, Leach - who cannot wear contact lenses because he suffers from astigmatism - managed to dictate the pace of the game throughout his stay at the crease.
"I just have to make sure they are clean every time they were facing up because I would really regret it if it had been smudged," he said, "and then they zoom in on the glasses and say 'he didn't clean his glasses'.
"I just had to stay calm and do the job at hand. I felt good out there, I was really focused on what I needed to do."
Generally left to face a ball or two at the end of an over, Leach left, ducked, weaved and defended his way out of trouble. "I got on with it," he said, "and it [the target] quite quickly seemed to go down. Suddenly it's eight to win, and you're like 'oh my God'.
"It is all a bit of a blur to be honest. I didn't want to get in Stokesy's bubble when he was doing really well, hitting those sixes. I didn't want to say too much but I also wanted him to just focus on the next ball, especially when we got close.
"He said in the changing room that he got nervous when it was down to eight. It seemed so close but the way we were playing it was still quite far away. I just wanted him to focus on every ball, and if it was there he would hit it for six."
There was, of course, the run-out-that-wasn't. If Nathan Lyon had managed to gather the ball as Leach found himself stranded halfway down the pitch, the narrative around his innings would be starkly different.
"That was not a nice moment," Leach said. "There were two balls left so I thought [Stokes] might squeeze a single so that I could face one and he'd have the next over. But it's all good. I don't want to focus on that moment - I want to focus on running down to Stokes when he hit the winning runs."
And so he might. If his team-mates' hardships rarely seem to extend beyond a bad run of form, it is worth reflecting on the multiple setbacks that Leach has overcome on his ascent to the Test side.
He suffers from Crohn's disease, a bowel condition that is often triggered by stress. In 2015, he fractured his skull after fainting on his way to the toilet in the middle of the night. The next summer, his hopes of an international call-up were twice set back; first by comments from his county captain Chris Rogers that he was not "emotionally" ready, then by the news that routine tests at Loughborough had revealed an illegal kink in his bowling action.
Last summer, he found out he had broken his thumb the day before he was set to be announced in the Test squad to play Pakistan. A concussion suffered after being hit by a Morne Morkel bouncer then cost him the chance to prove his form ahead of the India series, and he was again left out.
Perhaps it is no surprise, then, that Leach revealed he thought he would "be watching at home" during this series.
"I wanted to be ready to play and not presume anything," he said. "It's been a tough lead-in because obviously the county cricket has been all T20 stuff, my last long bowl was the Australia A game [for the England Lions in July] which was quite a while ago. That's been a challenge but I've tried to stay ready through training, and my opportunity has come about so I'm trying to make the most of it."
If those comments are damning on the suitability of the county fixture list, they also serve to add to Leach's status as a normal bloke. To stay match-fit between the Ireland Test and his Ashes debut at Lord's, he went home to play for his club side, Taunton Deane. Once part of the Cardiff MCCU production line under Mark O'Leary, he is an example to every club, university, and county cricketer as to what can be achieved with sheer dedication.
It is important, too, to remember that Leach has bowled well in his two opportunities this series. Since Graeme Swann's retirement, England have longed for a spinner who can tie down an end at home; for all Moeen Ali's mercurial talents, he has generally been a wicket-taker rather than a defensive option.
So Leach's economy rate of 2.64 in this series has been just as important as his five wickets. Moving into the final two Tests, at the traditionally more spin-friendly venues in the country, he will be expected to play a role of increasing importance.
"I think I have more to offer with the ball," he said, "and hopefully I'm able to show that over the next couple of games. Obviously the last couple of times I've been doing media stuff at the end of games it's been for my batting, which is mad! I want to be helping the team out with the ball primarily, and I'm looking to bring my best to Old Trafford."
Matt Roller is an assistant editor at ESPNcricinfo. He tweets at @mroller98