You have to be kidding me. On both my Pixel and Pixel 2 my Bluetooth always worked, even in areas with a lot of RF interference and horrible propagation conditions. It's the only radio technology that I've never had a problem with on both phones where I've had WiFi and Cellular crap out on me and be completely unusable at different times.
Were you using FULL SIZE overhead earphones(maybe a larger antenna surface area)? Or actual earpieces and buds?
You might not understand just how badly I wanted to keep these pixels, since the phones I had before were total nightmare experiences (Asus - lies for years about updating the OS, Blu - just too slow low end model, Bloatware phones)>
I owned the Pixel 2 and 3 at the same time, fully updated, and actually thought I was getting defective earpieces from top vendors. Sony, Plantronics, and I was sending them back as broken! I feel so embarrassed now. When the Airpods wouldn't work i finally knew something was wrong. Since I was going to travel in a 3rd world country, I bought a $99 motorola phone to use on my trip. I tried the airpods & one cheap set I hadn't returned and with the $99 phone they worked 100% PERFECTLY WITHOUT FLAW, while totally unusable on either Pixel. That's when I got REALLY angry and immediately listed both Pixels on eBay with a warning to the buyer about how defective Bluetooth is.
I feel like there can be 1 bad phone or 1 bad headset and someone could argue against me then. . . but I tried so many permutations to see abject failure, I have 0 doubts. It's not 99% it's settled science that Pixel doesn't work.