Well, Sikorsky did exactly that 60 years ago with the Sea King
Ah, 60 years ago. That must have been a wonderful time, maybe we could just keep using Sea Kings ad infinitum? Nothing will ever be as good.
I think the "60 years ago" part is the key issue. I should perhaps have said no modern helicopter company. It's never going to happen as the O&G, charter, (passenger config aircraft generally) etc. market beats SAR everyday.
Just compare S92 in SAR usage to others? Same with AW139 and eventually AW189. SAR is not a big enough deal for a company to invest in the perfect solution.