Downsides of usb-c headphones:

1. Bluetooth security risk surface, exposes your phone to more attacks.

2. Most/all phones have a single usb-c port. Charging and using headphones difficult

3. Usb-c port placement is awkwardly on bottom of phone while must headphone jacks are on top of the phone. Plugging in your headphones on the bottom of the phone with a dongle is awkward.

4. The entire process of using a usb-c dongle or using Bluetooth headphones makes the entire system more complicated. KISS (keep it simple). The more complexity there is that can go wrong, the worse the experience. If I'm taking a important conference call, I want my audio to just work.

5. Bluetooth audio is delayed compare to wired

6. Bluetooth Microphone standard is quite poor, the sound quality when talking on a group calls is bad compared to wired.

Not directly related: the whole point of removing the headphone jack was to sell airpods. First apple, then android, and even fair phone. Each time the jack is removed to push sales of the branded Bluetooth ear buds. It's a user hostile move.

https://www.wired.co.uk/article/apple-airpods-success

The excuse may be to save money, Space, water rating, but the reason is increased sales.

I personally still use a pixel 5A which had a headphone jack only because it's the B tier phone for markets where people are less likely to also buy the airpods.