Is there any benefit to running the Verizon version on an unlocked pixel 6 pro?
The best answer is "maybe", leaning towards "probably".
For example, and probably a bad example but the only one I got. When I got my unlocked HTC 10 before I got the Pixel 1 in 2016, and I was still with Verizon at the time, I had no idea that I was going to have to jump through hoops to get Verizon's radio.img on my HTC 10, which was rooted so no big deal. Now maybe there was a whole Verizon firmware I could flash, but if I just wanted to use the regular unlocked HTC 10 firmware, I had to put the Verizon radio.img on there to even work on the network.
On the Pixels, I don't think it's ever been quite like that. I think you can use the regular firmware just fine on Verizon, but maybe, just maybe, it will work better with their proprietary bits that come with the Verizon version of the firmware.
Also, I know sometimes in the past that if you had the unlocked firmware on a device but used a Verizon SIM (or in other cases with some phones, an AT&T SIM, and probably applied to T-Mobile too), that you would then receive an OTA automatically to put you on their particular variant of the most recent firmware. So unless you disabled updates in Developer Options, you'd get the "proper" firmware for your usage anyway, and of course, being rooted is the ultimate method to avoid the proprietary variant of the firmware since OTAs will most likely refuse to even update a rooted device, although you should still turn automatic updates off since there's a chance it could instead soft-brick your device.