From what I understand......att has to provision the phone to use HD features....and your phone has to have the capability....and you have to have an HD sim....but they don't provision non att branded phones except iPhones bought from Apple. My theory is though.....if you have another phone that has HD capability....have them turn the features on then take that Sim and put it in the pixel...it should work.....I haven't tried it but I think it should work.
Also...the HD features only work if both ppl have the feature and have it turned on and are both on att network....a lot of things have to come together for it to work.
1). Common misconception is that AT&T "won't allow" VoLTE on unlocked/non-branded Android devices, but there are multiple parts to this. I see more often than not that a device that supports VoLTE in general just doesn't have the proper configuration for AT&T's VoLTE (read: the IMS profile isn't set up), not to mention the modem configuration doesn't support it. AT&T may have a whitelist for "advanced services" on their network that devices must be on to access them, but there are work-arounds (like you mention, SIM swap from a branded device to non-branded, for example). However, based on what folks in this thread state, that doesn't seem to be required.
2). HD Voice ≠ VoLTE. On AT&T's network (as well as Verizon's), VoLTE is required for HD Voice to be available, but just because a call isn't utilizing "HD Voice" doesn't mean it's not utilizing VoLTE. It's to be noted that AT&T refer to VoLTE as "HD Voice" as to minimize consumer confusion (similar to how Verizon has Advanced Calling 1.0, which is effectively the same thing). When a phone is provisioned for "HD Voice" on AT&T's network, calls complete over the LTE (packet-switched) network instead of the legacy UMTS (circuit-switched) network regardless of who's being called. I can call a landline/business/non-interconnected carrier phone number, and the call will always complete over LTE, but the
real HD Voice does only work if the recipient is on an interconnected network. Currently, Verizon and AT&T share HD voice calls for those who meet the networks requirements (proper SIM card, account and SIM provisioned for VoLTE, supported device).