And yet the 21-year-old still cut a frustrated figure as the physicality of tennis, rather than the game itself, yet again proved his undoing in a 6-3, 3-6, 6-3, 6-4 fourth-round loss to No8 seed Andrey Rublev.
A lack of match fitness in an injury-hit season eventually led to Draper's undoing as the match wore on in the heat.
Last night's loss ended British singles hopes in New York for yet another year, but Draper warned his peers he expected to make it to the very top of the men's game before long, once able to finally get rid of his injury gremlins.
"With the amount of injuries I've had and the amount of times I've not been able to compete — and I've had difficult times in my career — it has honestly been tough to believe I can go all the way in a grand slam right now," he said. "But if I just can get things right, still be able to compete and train, I think I can go all the way in this sport, 100 per cent.
"It's not my tennis holding me back, it's my physicality and staying on court consistently. Once I do that, I think I will prove to myself that I will be able to be one of the best players in the world.
"My tennis is right there. I've barely played in the last couple of months and I've come here, made the fourth round and pushed a top-10 player.
Prior to the US hard-court swing, Draper had not played since pulling out injured from his first-round match at the French Open at the end of May with a different shoulder issue to the one picked up in the States.
The lack of game time has seen him plummet from just outside being seeded at a grand slam at a career-high 38th in the world to being outside the world's top 100 in the lead up to Flushing Meadows. His run to the last 16 ought to see him on the verge of breaking back into the world's top 100 once more.
During his time out of the sport, Draper revealed that world No1 Carlos Alcaraz, among the favourites to win the title in New York, had been quick to check in on him with messages, as well as offering any support possible.
Victory for the British No4 would have resulted in his first grand slam quarter-final appearance, but it was still his best run at a major, having not made it past the second round previously in his nascent career.
Following the loss, the big-serving left-hander, who has been tipped by an array of pundits and peers to make it to the very top of the game in the future, said his focus was on getting his body right for the remainder of this season and into 2024.
"The first couple of sets were a battle and I started to struggle physically after I broke him in the third set," he said. "I gave it all I had mentally, but I was pretty drained.
"That's where, now that I'm fit, we can go back to base and try and work each day to be better with that intensity. It's tough when you've been out so long and have no feedback. I can train with more intensity now remembering that match and how knackered I was after it."