I appreciate that MS is trying to keep things simple by not having two competing systems (something they often don't do, think Teams and Skype, which are still fighting with each other today), and clearly the ChatGPT-based system is better. However, I think this misses a significant marketing opportunity to fold the better AI into Cortana. The only people who care about the name Cortana are her fans, so even if perception is that Cortana lost, there's no real downside to just promoting it as the ChatGPT technology to the rest of the world. That furthers loyalty among the few fans.
A personified brand will almost always inspire greater loyalty than a technical term (most people tend to feel more attached to friends than things and why marketers like to create brand mascots -- tough to do, but very powerful once the market associates the mascot with the product). And obviously while the AI tech of today is much better than a few years ago, and similarly, the AI tech a few years from now will obsolete what we use today, they shouldn't rebrand it and start over every time the underlying tech improves. Therefore, MS should build out a powerful Cortana around ChatGPT 4.0 now, and going forward just let Cortana be the name, face, and voice for whatever the current AI query and support system is. This would be the simplest and most effective way to generate brand preference for MS AI.
This would just be smart marketing. Another missed opportunity for MS.