I went solo in 2009 for dinner and enjoyed it. Obviously, it was a long time ago, but other than enjoying the meal, I remember that the monorail went down and I had to take the boat to the Polynesian. With the monorail, every boat to the resorts was backed up. By the time I made it to my check in time roughly 45 minutes after I was supposed to be there, the CM apologized for my stress and checked me in. I think they seated me in 5 or 10 minutes.
Having made 2 solo trips to WDW and now planning a 3rd, I've never had an issue dining solo, including character meals. If you want to try a place, don't worry about dining solo and give it a try.