Kurtzman began his association with Star Trek as a producer and writer on the JJ Abrams-directed movies Star Trek (2009) and Star Trek Into Darkness (2013). He was recruited by new streamer CBS All Access (as it was then) to help Bryan Fuller and his team helm the first Star Trek television series in over a decade, Star Trek: Discovery (2017-present). Fuller left during pre-production, reportedly over budget and creative issues, and Kurtzman was promoted to showrunner. With Star Trek: Discovery a huge hit for the nascent streamer, Kurtzman has overseen the franchise's expansion to incorporate multiple spin-off shows: Picard, Lower Decks and the to-debut-shortly Prodigy and Strange New Worlds. CBS and Paramount merged last year, with CBS All Access being rebranded Paramount+. It seems that the new corporate overlords are happy enough with the franchise's popularity to retain Kurtzman's services.
However, Kurtzman has proved a divisive figure with long-term Trek fans, due to a relaxed attitude to continuity and a perceived focus on cutting-edge visual effects over character. A repeated criticism is that major character development too often happens off-screen, and sometimes audiences are asked to care about the fate of a background character who's barely uttered a line of dialogue on-screen. His plots are often incoherent and muddled. However, some of his work has been better received; Lower Decks, in particular, has attracted critical and fan acclaim for its respectful-but-fun take on Star Trek's mythos. It also sounds like Kurtzman is adopting less of a direct role in each show to focus more on the business of running the whole franchise, with individual writers and showrunners much more responsible for each show. It sounds like he's becoming more like Rick Berman once Deep Space Nine and Voyager launched, entrusting shows to individual writers whilst making more big-picture, financial decisions behind the scenes.
It also sounds like active development has resumed on several projects previously put on hold. Kurtzman had indicated that five shows was a "sweet spot" for Star Trek and he didn't want to put another one on the air until one of the existing shows - probably Picard, since Patrick Stewart (who recently turned 81) is unwilling to play the role for a long run - reached a natural conclusion. However, the article suggests that they have resumed development on the Michelle Yeoh-starring Section 31 and an unusual new take on Star Trek, focusing on the Next Generation/Deep Space Nine character of Worf.
According to ill-informed YouTube channels, Kurtzman has continuously been on the edge of being fired and his shows cancelled for the past four years. No doubt they will continue to report that this will be the case.