But when he did, finally stopping at an Ineos team mini-van in the back streets of central Pau and with a cloud of reporters in hot pursuit, it was to recognise he was as surprised as anyone else, albeit cautious about the long-term consequences, at Julian Alaphilippe's time trial win.
"I didn't expect that; he's obviously going incredibly well," Thomas told reporters. "He's certainly a favourite and one to watch at the minute."
The second-to-last rider to start on the 27.2km course, Thomas had crossed the line provisionally with the fastest time after ousting Thomas de Gendt (Lotto-Soudal) by 24 seconds.
But less than two minutes later, even as the Team Ineos leader was catching his breath, Alaphilippe (Deceuninck-QuickStep) crossed the line 14 seconds up on Thomas and the Welshman was the first to admit this was not how he thought the stage might pan out.
A winner of the Tour's time trial back in 2017, which automatically propelled him into yellow as it was the opening TT, Thomas had started Friday's stage 72 seconds down on Alaphilippe. The challenge of taking the lead for a third time in three years looked like a very feasible one.
However, as Thomas explained, he wasn't on a bad day but not on a particularly good one either. In the final part of the time trial, where he expected to be able to pull out all the stops on the flatter part of the course, his body failed to respond. Instead, Alaphilippe, having been just six seconds ahead on the previous time check, managed to more than double his advantage on the run-in to Pau.
"I felt it was all under control, but in the last eight kilometres, when I wanted to step on it, I didn't have that last five percent," Thomas said. "It's still a decent ride, but…"
Nor, in fact, was Thomas' advantage on most of the the rest of the field that close to most predictions, even if he did manage to gain time on all of them. In a graph spread across two pages this morning, L'Equipe newspaper forecast that he would gain 57 seconds on Steven Kruijswijk (Jumbo-Visma) when in fact Thomas' advantage was 31 seconds.
Equally, Thibaut Pinot (Groupama-FDJ) was expected to lose 82 seconds, and the damage done was only 35 seconds. Perhaps most significantly, given the results, for Alaphilippe they just had a headline of 'a case apart' before explaining it was impossible to make any realistic contrasts between the two's previous TT performances.
For all the French euphoria surrounding Alaphilippe, it's worth remembering this is only round one of three big GC challenges this weekend, given there are two major Pyrenean stages to come. It's also worth remembering that Team Ineos were keen to point out in the team time trial, where they also came second, that their riders had been focussing on their climbing during their pre-Tour buildup, not racing against the clock, given the amount of high mountain stages in this year's race.
Given the number of incognitos and possibilities this result throws up, therefore, Thomas was perhaps understandably guarded when asked if he believed Alaphilippe could go all the way to Paris in yellow, saying, "For sure, the way he's riding, if he can keep that up he'll win. But there's a lot of hard stages to come."