I'm happy in my 35-year marriage, but if I were to find myself alone, alone is how I'd live out my remaining years. Most of my older friends who re-married wound up having to take care of the spouse instead of enjoying life. I also don't intend to have to worry about my kids and grandkids maybe not getting all my estate as intended, and we found with a great-aunt who re-married at 74 that pre-nups aren't entirely effective.
A companion would be nice, but so is solitude by choice, freedom from legal hassles, and financial independence. Even a happy marriage takes a lot of energy, and I just wouldn't want to spend that much again. Too much to do for myself, friends and family without being weighted down!