Shooting two guns at the same time sucks whether it is at one or multiple targets.
You can't look down the sights on both at the same time, and the recoil is goofy because you can't line both up with your body if aiming at the same target. So you are either shooting one blindly or two awkwardly.
I don't remember exactly because last time I saw the Matrix was two decades ago but i had the impression that Neo didn't shoot exactly at the same time but alternating, although at superhuman speeds
Edit: yes the handguns were shot alternately https://yewtu.be/watch?v=Z2eCmhBgsyI (at around 1:10), but automatic rifles and uzis were shot at the same time