Barclay hinted the ongoing cycle could be the last for the ambitious concept.
The nine-team league competition has been ruined by the dangerous pandemic, resulting in indefinite suspension of quite a few bilateral series.
The raging outbreak forced the ICC to recently adopt a percentage-based points model in order to keep the tournament on track for a scheduled 2021 Lord's final.
During a virtual media conference for 'wire services', Barclay was asked whether the championship has proved to be the fillip that it was meant to be for Test cricket?
"In short, I don't think so," he responded. "The COVID has probably highlighted its shortcomings of the championship."
"The issues that we have already got, I wonder whether some of it was because of an attempt to develop a Test Championship, clearly designed to drive interest back into Test cricket, provide a bit of context and relevance around the Test matches," added the New Zealander, suggesting the well-intentioned idea has flopped in practice.
"From an idealist's point of view, probably it had a lot of merit but practically, I do disagree, I am not sure whether it has achieved what it intended to do."
So bemused he is with the concept that Barclay hinted the ongoing cycle could well be the last for Test championship.
"My personal view is let's get through with the little bit that we can in this COVID-19, with reallocation of points and all that," he said.
"...but once we have done that, let's go back to the drawing board as I am not quite sure whether it (WTC) entirely fits the purpose and has achieved what it intended to after being conceptualised four to five years back."
"I think we need to look at it in context of calendar and not put cricketers in a situation where it's a lot more worse and not going to help us."
To back his point, Barclay said quite a few full member nations can't afford to play Test cricket, a longstanding issue borne out of financial inequality in the world game.
"Yeah, I think there would be some countries. It is difficult for some of the full members as they simply can't afford to play Test cricket."
"Test cricket has got its legacy and I am a purist but I do accept that as much as I want to keep it as it is, less and less countries are able to afford that arrangement and are able to play it."
"Very few countries can make it work from a financial point of view."
With a growing number of T20 leagues, the cricketing calendar has only gotten more congested, with member nations, outside India, England and Australia, finding it extremely difficult to manage all three international formats.
"My view is that, I think all forms of cricket need to be taken into account. You are right, the calendar is increasingly becoming congested and something has to give in somewhere," said Barclay.
"But I do respect that each country has the right to develop its own domestic league given it meets the ICC requirements and is properly sanctioned."
"Clearly there is a demand from the playing point of view and commercial partnering perspective. So let's accept that domestic leagues are here to stay and they have been tremendously contributing to the growth of the really exciting product like the IPL, BBL and CPL."
Barclay suggested managing bilateral cricket with added context and keeping a balance in order to maintain players' physical and mental well-being will be his priority.
"It's an incredibly difficult juggling act to get in there and also, we need to have enough conversations regarding players' health safety. I don't think we have had enough conversations," he said.
"Some of the focus needs to be on the integrity aspect of the game and we need to have competitions which are relevant and have context."
With his arrival, it's highly likely the controversial proposal for more ICC events in the 2023-31 cycle has also seen a silent death.
"Bilateral cricket is fundamentally important to member countries. ICC runs very, very good events, all countries must have an opportunity to take part in these events," Barclay said.
"I am a fan of maintaining ICC events which are world class but at the same time, giving an opportunity to members to have bilateral cricket."
On India-Pakistan cricket, Barclay clearly stated it's "not his mandate" and the resumption of two nations' bilateral ties depends entirely on "geopolitical" changes.
There have been issues faced with the BCCI when it comes to India's share in the ICC broadcasting rights money, but Barclay said it's important for the world governing body to recognise and resolve the problems put forward by the mighty full-member.
"India is a massively important part of world cricket. Like all families, we have general squabbles but India recognises that ICC needs Indian cricket. We have been able to navigate through differences if any," he said.
(Inputs from PTI)