Those "helmets" exist, but helmets as such are used in commercial diving with a tether to the diver. Not very practical to have it running along the cave for multiple divers. The full face masks that allow that are mainly used in open circuit diving and are bulky. I don't know if the pros/cons would make a huge difference.
At one point I believe Tesla or just Musk were planning and developing a pod to carry each boy, but the tunnels and sumps were so narrow that they wouldn't be able to make the turns.
Having tunnels with compressed air to inflate them would have similar issues with the bends. Not to mention the amount of gas and pressure needed to displace all that water.
I guess they took the most direct and logistically available option. I'm sure it will be a case study for the future.