I thought the point of these policies was to cover you in the cases of long term disability when you lose the ability to work in your field for extend (6+ months) periods of time. If your FI, I can't see why you would need a policey but if you aren't then it becomes a question of how paranoid are you.
It seems that a nicely funded 3-6 month emergency fund would make these kinds of policies unnecessary.
My point is this: The cancer policy I sold was about 18/mo, for essentially up to 150/day in benefits, and double for icu. The stroke was another 5/mo rider on that (this was a while back, so it might have gone up since then). so, for 2760 (about 10 years worth of coverage), you have a policy that during that time can pay you, like some of the clients I had, about 3k-22k in benefits. Cancer treatment, if successful, usually only has you down a few weeks; once you start certain treamtents, you could go back to work. But WHILE you're down, you can't be on disability (it's short term, usually doesn't qualify unless long term) or unemployment (you're employer would have to let you go the day you check into the hospital, which is likely grounds for a lawsuit, and most states you have a waiting period anyway before you got benefits), so you have 0 income, and treatment may be 5 figures, even WITH insurance! If you can save that amount, that's fine, but I can tell you I would rather pay 2760 every ten years, and keep my 10k, than try to save 10k (It's gonna be more, I'm low balling) for a stormy day like that, and then hope it won't hurt my FI. The insurance isn't going to make being diagnosed a 0 cost, but it helps at a time you're basically getting a kick in the face.
Most insurance is designed to give you more than you pay. Best example: term life. You will NEVER pay enough into a 500k policy to make it cheaper to save the money yourself, even if your parents buy it when you're 0, and you keep it till 100, renewing at the higher rates it steps up to as you age. These supplimentary policies work on that principal. They're cheap, and yes, they're specific, but when you have one and need it, you'll never be mad for paying for it for 20 years. I personally don't like accident policies, because depending on the industry you're in, they're worthless. I do construction, and I can tell you an accident policy for me 25/mo probably pay 25-50/day for hosp stay, so it would be worthless to me.
One more point: if you get aflac through work, it'll be cheaper than you can buy it on your own, and you can keep it after you leave if you want.
Insurance is one of those things us people get to avoid catastrophic loss. Millionaires and billionaires carry insurance against frivolous lawsuits and even kidnapping; you really think if they have that much money, they would spend money on something they don't need, when it may cost 4-7 figures (depending on their worth) to have?