There are probably multiple reasons people can come up with for sticking with grass but me being a soccer guy must bring up what I know about the situation.
The dolphins owner has been quoted as saying he wants to bring in more big name soccer matches to the stadium. Not only friendly (exhibition) matches Like Real Madrid and Barcelona that sold out the Stadium this summer and generated some revenue...
... but he also wants to be a part of any future Gold Cups, Copa Americas and most importantly the World Cup bid in 2026.
Field turf would basically kill any chances of hosting those tournaments so I think that is a factor. Maybe not the main factor, but a factor.
Forty-One Cities Across Canada, Mexico and the United States Submit Bids to Serve as Host Cities in United Bid for 2026 FIFA World Cup - U.S. Soccer
Edmonton, Montreal, Ottawa, Regina, Vancouver, Atlanta, Birmingham, Foxborough, Minnesota, Houston, New York, Indy, Detroit, Seattle, Dallas, Orlando, Salt Lake City and San Antonio all submitted bids with artificial surfaces.
So probably not as big of an issue as it could be.