I think this can be likened to a police search warrant. Unless there's strong evidence of Covid originating from the lab, others have so strong justifications to search the lab. After all, nobody likes their places invaded, even though it's in the name of cooperation.

At this point, there's no strong evidence that Covid came from the lab. The Wuhan lab only worked with coronaviruses similar to 2003/2004 SARS1, not Covid-19. The closest virus to Covid-19 the Wuhan lab has was RaTG13, which is just 96% similar to Covid-19, equivalent to decades of evolutionary gap.

Moreover, no early confirmed cases of Covid were found near the lab. (The 3 sick Wuhan lab researchers are not confirmed cases btw since subsequent governmental efforts failed to confirm this info.) Therefore, in short, evidence is simply inadequate to issue a legal search warrant into the labs.