I seriously doubt that you will be able to find an insurance carrier that does NOT have a 24-hour hotline these days. It's such a highly competitive field that they all want your business--any way they can get it. Look at the way auto insurance has gone in the past 20 years. Two decades ago they all claimed they were loosing money on auto insurance. Today, those same carriers are spending hundreds of millions, if not billions of dollars in advertising their car insurance.
Fortunately, I've only run aground (softly) twice in more than 55 years of boating. Both times I was in a well-marked channel, and I was able to extricate myself in just a few minutes.
One of the locations was Chincoteague, VA, where recent storms had caused a sandbar to shift more than 100 feet out into the main channel. The Coast Guard knew about the problem, apologized for the mishap and actually came to my rescue and towed me to deeper water.
The next location was the Havre de Grace, MD channel which is quite narrow when there's a tug pushing a pair of side-by-side barges near the turn at Battery Island. I gave him a wide berth, eased about 50-feet out of the channel near the Sand Island and came to an abrupt halt. As the tug passed his wake actually lifted me off the bottom, which made it easy for me to motor off the soft sand.
Hopefully, since I purchased the Morgan 33 O.I., which only draws 3'-11", groundings will be even less of a problem. But, if it happens again, I have Boat U.S. unlimited towing package, which I hope never to use.