Van der Poel lit up the opening days, winning stage 2 at Mûr-de-Bretagne to take the yellow jersey, which he relinquished after the first day in the Alps.
The following morning, he announced he was heading home in order to prepare for the Olympic Games in Tokyo later this summer, where he will compete in the cross-country mountain bike race.
Five-time Tour de France winner Eddy Merckx, who kept Van der Poel's grandfather Raymond Poulidor on the lower steps of the podium in three of those Tours, couldn't see sense in the decision.
"I couldn't do that. If you start a stage race, it's not with the idea of getting out," Merckx said, according to Belgian broadcaster Sporza. "Otherwise you have to prepare for the Games in a different way. That does not benefit cycling."
Van der Poel's visit to the Tour de France comes amid a busy 2021 schedule that started with him winning the cyclo-cross world title and then switching to the road for the Spring Classics. The mountain bike, however, has always taken priority in the Dutchman's mind as he hunts an Olympic title, and his visit to the Tour - on his Alpecin-Fenix team's debut - was always likely to end prematurely.
"Van der Poel himself is asking for such a full schedule. Nobody forces him to do all that," Merckx said.
"The Tour de France is the biggest race of the year and in cycling, I think it's a pity."
Merckx was, however, more generous when it came to Van der Poel's performances during his short stint at the Tour.
"What he did on the Mûr-de-Bretagne was magnificent. Grabbing the bonus seconds on the first passage and the victory on the second, then you have to be really strong."
However, he dismissed any notion that Van der Poel could one day develop into a Grand Tour contender.
"I went to dinner with Mathieu van der Poel and his grandfather Poulidor. Pou-Pou was convinced that Mathieu could win the Tour. Unfortunately, I have to say that that is not possible."
Merckx was also asked about Mark Cavendish and the prospect of the resurgent sprinter catching his record of 34 Tour de France stage victories, having won two so far to move to 32.
"To be honest, I no longer believed in his comeback. Miracles can sometimes happen in cycling. I think that's such a miracle."
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