Batwoman’s kryptonite story creates an Arrowverse plot hole in season 2. This season of Batwoman has been heavy on the Kryptonian mineral in a storyline started in the first season. In season 1, Kate Kane was entrusted with the alien space rock for safekeeping by Kara Danvers during the “Crisis on Infinite Earths” crossover. In season 2, Ryan Wilder was shot with a kryptonite bullet that subsequently poisoned her and led her to the brink of death. However, the use of kryptonite in Batwoman leads to a glaring oversight within the Arrowverse at large.
Kryptonite has long been known to be detrimental to Supergirl and Superman. The green rock is capable of knocking them out, weakening them, and causing hallucinations if it enters into their bloodstream. All told, kryptonite is incredibly deadly to Kara and Clark Kent. Kate wanted to know whether or not she should destroy the kryptonite she had to avoid falling into Alice's hands, which is why she visited Supergirl in National City at the start of Batwoman season 2. Shortly after, Ryan was shot with a kryptonite bullet during a fight with Tommy Elliot. However, Batwoman, Luke Fox, and Mary Hamilton opted to get a hold of the desert rose, a magical flower capable of curing every ailment and disease instead of reaching out to their Kryptonian allies.
The plot hole stems from the dropped story thread from earlier in Batwoman season 2. After all, the crossover made a big deal about what having kryptonite could do and how dangerous it was — not just to Kryptonians, but to the world when in the wrong hands. Many of the scenes discussing kryptonite during the crossover were shared between Kara and Kate, who then relayed this information with Luke and Mary at the end of Batwoman season 1. To then have an entire subplot involving kryptonite poisoning in season 2 and not calling either Supergirl or Superman — both of whom are in close enough proximity now that they live on Earth-Prime following the events of “Crisis on Infinite Earths” — seems rather negligent. This is especially true considering Ryan’s rapidly deteriorating state. She didn't have that much time left and the plot that eventually took her to Coryana, an island hidden from the known world, sidestepped the most obvious solution.
Finding the desert rose, which bloomed on the obscure island, was a long shot. At the very least, getting in touch with Supergirl could have given the Bat team an idea as to what they were dealing with. An offscreen phone call and a few lines of exposition would have worked wonders in this instance. It would have, at the very least, confirmed that Luke and Mary had attempted to exhaust all avenues to get Ryan the help she needs. What’s the point of having Supergirl on speed dial if no one’s going to bother getting in touch? Of course, it’s possible that the originally planned crossover between Batwoman and Superman & Lois was meant to focus on kryptonite, and Clark may have worked alongside the Bat team to help and even cure Ryan’s kryptonite poisoning.
However, plans for the crossover were canceled due to the global pandemic. That said, considering Batwoman carried on with the kryptonite storyline, the show shouldn’t have made a magic flower Ryan’s only hope. What’s more, the lack of communication with Supergirl makes Batwoman feel less connected to the other Arrowverse shows. Whereas Black Lightning called The Flash (offscreen) for help with his daughter Jennifer’s situation, Batwoman seems to have forgotten Supergirl and Superman’s existence altogether. It’s even more of an egregious oversight when considering Kate thought to get Kara’s opinion about the destruction of kryptonite in season 1. The series may have lost Ruby Rose as Kate Kane, but that doesn’t mean it has to lose its ties to the shared universe or the other superheroes dwelling in it.