Yeah from the Android platform side it would be weird to build chips. For products like the Pixel phone though, that would be a great place to innovate. And realistically, Google needs to get into the custom chip game sooner rather than later... GCE needs to start competing with Amazon's Graviton ARM processors. The sooner you get the expertise and talent to churn out chips (and maybe even a fab or two?), the better. The global shortage for fab usage and chips could kind of force your hand soon.
Google doesn't have the volume on its first-party hardware to drive something like this yet & they would never start with BLE chips. Additionally, there's some really good vendors out of China already challenging BCOM & QCOM FWIW, which further complicates the "build it yourself" narrative (look at the Pixel buds which have an AirPods-like experience running a Chinese BLE chip for the buds which other Western vendors weren't able to match).
The Android org generally isn't the right org to build hardware, let alone do chip design. Maybe the camera team got closest when I worked there?
Source: worked on Pixel Buds @ Google & was one of several engineers responsible for selecting the chip vendor. We got source access to the entire stack/OS except for the microcode & some parts of the stack they hid. I found BES a way better partner to work with than the BCOM/QCOM mess.
Are you talking about the 1st or 2nd Gen Buds? Because the 2nd gens seem to have severe connection issues:
a) they frequently flip flop between at least two BT profiles, leading to a lackluster listening experience
b) they lose connection to each other (leading to intermittend profile switches during reconnects, possibly due to lack of available bandwidth)
c) they have severe signal quality issues, leading to limited range and audio interruptions
All these issues only happen with the 2nd Gen Pixel Buds, but not with a random sample of various other true wireless earbuds (I tested Sony WF-1000XM3, 1More True Wireless ANC, Airpods Pro) leading me to believe that this must be a hardware issue on Google's side, especially because the amount of people with the same issues is pretty high.
No other pair of true wireless earbuds hat any issues with music playback while I'm on a road bike, with my phone being on my back, only the Pixel Buds do - and I'm on my 2nd replacement already.