We've spent a great deal of time on Tom's Island when my kids were young and now hit it maybe every 4th or 5th trip. I read a lot of trip reports and most do not include their time on Sawyer Island. Wait time is almost always 5 minutes usually the wait for the raft to return. Over the years attendance has dwindled and normally there is only one raft running, the line usually occurs waiting for the raft on either end. They even shuttered Aunt Poly's quick services years ago. Vending machine replaced it for beverages. They tried to open it for spring break a few years ago with peanut butter sandwiches, turkey sandwiches, hummus, veggies and cold beverages but they didn't even serve soda. If it has ever popped up again I haven't seen it though they use to serve Fried Chicken in a cast iron pot meal long long ago.
I can't argue popular 'cause it is popular with those who return to the island but popular as far as volume of guests per hour per day is low. The only attraction with a shorter wait time is the Tree House. But the point of the rumors and also what I do understand is the square footage of that entire body of water and island. Further if they redevelop Liberty Square Presidents through the store area and including Horseshoe and Rifles they can build different type of land where more guests can be pumped through and are far more exciting to the masses. The River Boat is also popular with the repeat riders but it too has very few visitors per hour per day. Presidents can hold nearly 700 people but is rarely even close to that. Add in Sawyer and River Boat are only open limited hours each day usually 10-4, busier times 10-6. Little by little Disney closed a couple other water adventures there too over the years. Add in the liability of not guarded open-ish water, gators, the flooding tunnels in the Fort, ADA is a real stretch.
I have little doubt there are proposals to redevelop this area at some point. The Island could easily become either seasonal or go on a forever refurbishment along with the Riverboat. I am equally surprised the the Tiki's are still in the MK as everytime I've been in there in the last 10 years it has a few handfuls of people in there and usally half of them walk out during the show. Liberty takes a large footprint of the MK yet the portion that is rumored to be redeveloped in the future lacks the overall attendance averages to argue keeping it. I like Tom's Island, it was great for kids to run around when little. My Mom has issues with it as many of the walkways are steep and the raft she really needs a railing to cling to. BTM capacity per hour is 1500, Splash 1200, SM 2000, PotC 3200, UtS 2200, IaSW3000, Dumbo 1000 So from what I've read over the last 5 years or so is the popularity being how many people actually take in an attraction and will repeat it due to its popularity.
My agreement is I ride the boat, see the Presidents or float to Tom's about every 5 years. I have a few attractions like this in every Disney Park. I like Tom's just not every trip and certainly not for me multiple times a trip. Likely no matter what this area is may someday be redeveloped into the Mansion can likely be themed into the new development. I think the area has its traditionalists, but like with the Tiki's everyone was pretty much onboard they hated the once refurbishment, yet after the fire and it being restored still few find it popular enough to sit through in a day.