For those frustrated that their Uber app doesn’t work in East Hampton or at the prices charged for rides around Southampton in Uber black SUVs, Governor Andrew Cuomo’s announcement that he will press for an overhaul of state laws that make it difficult for the app-based car service to operate outside of New York City will be welcome news.

For residents and taxi company owners in Montauk and elsewhere on the South Fork, the long-expected news was met this week with apprehension.

“I think in some places Uber would work very well, but in the Hamptons, and especially in the summertime, I don’t see it working at all, so I’m not worried about it,” said Mark Ripolone, owner of Ditch Plains Taxi, which operates three cabs, primarily in Montauk. “When Uber was here a couple years ago they were charging rates three to four times more than us. That’s Uber, one word: greed.”

But one of the pedestals of Uber’s case, which it has lobbied state lawmakers to support for more than two years now, is that allowing Uber to expand would actually bring less expensive transportation options to riders all over the state.

In last week’s State of the State address, Mr. Cuomo sounded convinced. He laid out a multi-step proposal that would allow Uber and other app-based “ride sharing” services to contract with drivers outside of New York City, the only region of the state it operates in now.

“Ride sharing is bringing transportation into the 21st century and we are committed to ensuring that it becomes a reality statewide,” the governor said. “It provides economic opportunity and a cost-effective alternative to transportation, and we must ensure that all residents outside of New York City have access to its benefits.”

Foremost to the legislation would be lifting a current state law that prevents a company from providing blanket group insurance on cars it does not own.

That law has been the main impediment to Uber operating across the state since it blocked the company from providing the $1 million in insurance the company grants to all its drivers, the vast majority of whom are not professional cab drivers, when they are picking up passengers. To date, the only drivers Uber has contracted with in the state are full-time drivers who pay large sums for New York City Taxi & Limousine Commission, or T&LC, licenses, and carry the robust insurance coverage that requires.

The governor’s proposal also asked lawmakers to give the State Department of Motor Vehicles overarching licensing powers for taxicabs and livery vehicles—smoothing over the current jumbled landscape of myriad and varied local municipal licensing requirements, something Uber has said makes trying to operate a statewide service prohibitively complicated.

Those two proposals, if written into law, would likely bring Uber back to East Hampton and expand the company’s presence across Long Island. In East Hampton Town in particular, New York State’s laws had caused friction.

Beginning in about 2014, the burgeoning demand for taxis in the Hamptons and Montauk in particular began drawing some of Uber’s New York City-based cars to the South Fork on weekends. But because the drivers were mostly from New York City, they were often found sleeping in their parked vehicles in hamlet downtowns between the busy nighttime hours.

East Hampton amended its taxi licensing laws to require that a license be issued only to a car registered to a business address within the town. Uber was prevented from contracting with locally-registered drivers by the state’s insurance limitations and, after a brief publicity campaign directing outcry toward town officials, disabled the app service in the town altogether.

Uber managers have said the company expects that if the insurance limitations are lifted, the company would be able to contract with East End car owners as drivers, and that it would not spur a return to the issues seen with transient drivers in the past.

While most of Uber’s drivers are part-timers, lifting the insurance restrictions could mean that some small cab companies could contract their cars with the Uber app-based dispatching in addition to the standard local telephone dispatching and hacking at train stations, bus stops and busy nightspots.

Some cabbies said they would not welcome such a partnership and worry that a flood of new amateurs would rob them of business.

“I don’t have any interest in working with them,” Paul Acevedo, owner of Montauk’s Best Taxi, said. “The app stuff doesn’t work in Montauk. When Uber was out here the reason they got ousted was that the app wasn’t working for them and they were getting caught picking up people at the train station. They were back-dooring outside the app system. But that’s what you have to do at 4 a.m. on a Saturday when people are coming out of the clubs.”

Other companies have already begun using their own app-based dispatching. Mr. Ripolone’s company is entering its third season of booking rides through a free app that provides features similar to the more widely known Uber and Lyft apps, allowing customers to store payment information and showing the location of a cab and what the fare will be.

“Eventually everyone is going to have to conform,” he said of app-based taxi dispatching. “Technology is at a boom right now.”

Town Supervisor Larry Cantwell said that if all it took for Uber to operate locally without causing problems was to lift the insurance restrictions, he would support that. But he worried that the governor’s proposal to give DMV licensing oversight could handcuff towns too much, and prevent them from tackling issues that are locally specific.

“I understand the problem the state is trying to address, but if it leaves us holding the bag for the problems it creates then it is ill-conceived,” he said. “It’s frustrating when high levels of government substitute their judgment for what creates a serious problem in a community like ours without consultation. For us, it’s not about we want Uber or we don’t want Uber, it’s about trying to keep decent order.”