The only second-tier game he missed during the Argentine’s tenure was the post-promotion visit to Derby County and the cause of his absence was never stated in brackets after his name in the time-honoured football reporting fashion, because there was simply no way Bielsa was ever going to utter the word hangover in a press conference.
Klich made it onto the Pride Park pitch that day but only to break dance upon it, having sat on the bench and enjoyed a hard-earned rest as his team-mates cantered to victory.
He was a vital part of promotion, a cog that made so many others turn as they were designed to, and even if his influence waned in the much more difficult environment of Premier League football, he still got the nod in 35 of 38 top-flight games last season, starting 28 of them.
With a top-half finish all but assured Bielsa rested the Polish international for the final two, deciding after a goalscoring performance at Burnley that Klich had done enough to earn another break and some breathing space before the Euro 2020 tournament.
There can be no early finish for the 31-year-old this time round.
As a frustrating campaign comes to a close, one that had him in and out of the team, ranked ninth in the squad for minutes played and substituted 19 times – sometimes quite visibly to his dissatisfaction – he will surely be a man Jesse Marsch turns to on Sunday at Brentford.
Against Brighton, even in a team that struggled so badly in the first half, Klich was arguably the best player on the pitch for the Whites until being replaced with seven minutes remaining in a surprise swap.
The man showing the most tiredness was Rodrigo, who had almost come to a stand still, and Klich still appeared full of running but it was he who made way for Sam Greenwood in a change Marsch believes worked out.
Prior to coming off, though, Klich showed more than enough to suggest the American needs to stick with him for the final outing and there’s an argument to be made that Rodrigo did not.
If Marsch is to continue to major on aggression and winning the ball back before moving it quickly in transition, then perhaps Lewis Bate accompanying Kalvin Phillips in the heart of the midfield, with Klich ahead of them, would give them more in terms of legs, energy and ball retention. What Klich gives Leeds, that Rodrigo does not, is the versatility to either operate in a box-to-box role or an offensive midfield position.
He will run all day, with and without the football, getting after opponents, darting into space, looking to go beyond. The Spaniard, by comparison, is very much a forward and after two seasons at Leeds it’s fairly safe to say that pressing is very much not his game.
It’s a safe bet that this game will have some needle – Pontus Jansson won’t be alone in naturally exuding it – and to fight a fire Ivan Toney has been stoking on Twitter with fire, Leeds will need Klich, their wind-up merchant in chief.
In the final third, Rodrigo can be creative but so too can Klich, who loves to take on a shot and looks for those incisive passes in and around the area.
He’s still well capable of supplying the pass before the assist, even if his output has dropped in a side struggling to attack this season.
In a match against a side who will look to Christian Eriksen for creative inspiration, Leeds need to set about their opponents from the off and for the duration and Klich is far more suited to that than Rodrigo is.
So too is Bate, a youngster with tenacity and ability on the ball that allows him to operate in the tight spaces that have become the Leeds United midfield in recent weeks.
Alongside Phillips and behind Klich, Bate could potentially help form a trio to match up against Thomas Frank’s midfield three, if the Bees line up in the 4-3-3 the Dane has been favouring again recently.
A consideration, of course, is the magnitude of the game and Bate’s inexperience. The Chelsea clash just looked too much for him, although being at Elland Road, up against stifling expectation as well as his former club, an early concession and Daniel James’ first-half red card were likely contributing factors.
And Rodrigo might have bags of big-game experience, along with an attacking X-factor, but the mini renaissance of March and April has come and gone and simply put, in a game so vital to the club’s immediate future, Leeds cannot afford to give the ball away as often and as cheaply as he did last Sunday.
If the £27m man was to drop out and Bate was to come in, it would place a huge onus and responsibility on Joe Gelhardt in the lone striker role. He’s not a targetman and you could see him forging a fine career as a second striker, but he does at least take shots on and makes things happen.
If, however, Patrick Bamford is somehow patched-together comprehensively enough to start, then the number nine in his natural spot with Gelhardt behind him would seem logical and, whisper it, quite exciting. Bate therefore would stay out, allowing Klich to operate in the middle with Phillips.
Elsewhere, Junior Firpo and Robin Koch on either side of Liam Cooper and Pascal Struijk would be a back four picked on availability and form – something Diego Llorente has been struggling to maintain – and the club only has two fit senior wingers so Raphinha and Jack Harrison are always going to feature.
There are big calls for Marsch to make, but not too many of them, such is the devastation of this squad by injury and suspension. Klich doesn’t feel like a big call, though. Just the right one.