There are low latency codex for BT that work well and if you’re streaming anyways, audio latency is the least of your concerns, like you’ve stated.
I just think that creating a “portable gaming handheld” without the option for Bluetooth is a crappy decision to not give gamers the option. The steam deck offers it, the variants offer it, hell even the switch offers it now.
I also think it’s even a worse slap in the face for PlayStation fans with Sony’s decision to make it so it’s not compatible with it’s current wireless PS5 headset and instead making their fans buy another set of headphones that cost nearly as much as their dumb terminal.