I think for certain properties influencers work, but certainly very specific. A FS GM told me over tea last year that for his property they get several requests a day from influencers, but they are very particular about who they work with (for this property this was true). They mostly come, do their thing with pictures and all that jazz and leave on to the next property -- interestingly they know next to nothing about the industry (there are exceptions), they can be quite demanding but in reality they get a solid room (not an over the top suite), a standardized amenity from PR (they call it press amenity) and breakfast.
What annoys me is that sometimes they don't even understand the property at all. They photoshop their pictures (many times not really flattering), and butcher these pictures beyond repair. We do not live in a candy colored world where everything comes in pastel colors and most properties do not look good with these filters. It is amusing that some post pictures which are in fact 5 years old... when you point out that this part of the hotel does not exist anymore in that form (due to renovations), they either delete the comment or just object... simply because they aim to give away the feeling of constant travel, while sitting at home in Dagenham with 4 roommates and 2 cats, saving for Rimowa x Supreme luggage.
There is a demographic which books hotels according to familiar Instagram stories, so yes they do exist and with the ever increasing hype of "experiences" in the industry, many hotels are indeed quite enamoured... however then please don't complain they account mostly for standard rooms through booking.com or lobby visits in which endless selfies are taken while disturbing other guests.
A well managed Instagram account is a necessity these days -- of course -- but somehow I quite like the understated elegance of various MO accounts, compared to the ostentatious influencer addiction of certain FS (hello George V). Not too long ago, most properties were quite "hush" about their guests. I recall that during a visit of a wonderful French-Canadian singer the team at George V wouldn't confirm the obvious to a guest asking, in the name of privacy (thank god). Last year they were apologetic about the disturbances in the lobby while casually mentioning that Kris Jenner made her way through the masses in front of the hotel. How things have changed!
FS usually have their PR Director/manager take care of individual property accounts, some properties have a dedicated social media specialist (George V for example hired young professional from beauty industry to take care of their channels and she specializes in Influencer marketing -- this was after Florence Dubois' departure). Peninsula also recently jumped on the train. The latest I heard regarding hard numbers is that it is very difficult to estimate them, but actual bookings made solely because of influencer exposure are very low (though rising). Often especially millennials these days know the best hotels, though then find comparable (lesser) choices online or AirBNB.
I am personally most happy to be in a hotel or resort and not have to see a camera or a drone.
Some destinations prone to social media are (in no particular order): Mexico, Caribbean, Vegas, Bora Bora, Maldives, Seychelles, Paris, London, Marrakech, Hawaii, Greece (Mykonos, Santorini). Well known and somewhat exotic, but still mass market to appeal to as many as possible.