Cell reception will notoriously be spotty on the ocean. Also they say that the shark leads them to deeper waters and more away from land. So cell reception can become more restricted. Or Shaw can merely forbid them from getting phones onto the boat.

Speilberg can adapt to moden times. If anyone can, it would be him. But I don't know. That's why he is restricting himself to period pieces i guess.

When you consider Jaws, Shaw was adamant he would be the one to catch the shark. He knew the dangers. It was more a vendetta for him.

That's why the flashback was there. He was hunting the shark on Amity in retaliation for the death of his navy buddies.

So even if his boat was equipped with all the modern communication devices and come to think of it Shaw would not do. His character is more a salt of the earth kind), he would not ask for help. That's why when Brody called for the coastguard, he smashed the radio. He has to be the one to kill the beast.