While I can't refute your excellent financial discipline in saving for a "rainy day". I will point out that scratching up a few tens of thousands of dollars is not in the cards for most people.
"Scratching up a few tens of thousands of dollars" is hard for people in the early phases of their adult lives, but should definitely be in the cards for just about anybody nearing retirement age whose life hasn't taken a long series of unfortunate turns.
While I have not sold any cancer policy's in my short career, my wife has sold many. And she has many testimonials of crying people who come to her thanking her for selling them a cancer policy after they or their loved ones have come down with cancer. And she herself benefited from her own cancer policy.
I see tons of testimonials from people explaining what a great deal their appliance insurance, third-party auto warranty, or electronics "protection plans" are. That doesn't make it true. Let's try to make this a data-driven conversation instead of dealing in anecdotes.
If you have the discipline and the wherewithal to insure yourself that is fine. Most people don't. And telling a 60 year old that if they take that $30 a month in put it into a savings vehicle, in 20 years they will have what a specified disease policy will pay up front for a diagnosis for the covered disease is true, but what about the ongoing payments for each covered procedure?
If they're starting to save at 60, they're already doing it wrong. As for the ongoing payments for each procedure, that's what proper medical insurance is for. There is a lot of health insurance available that provides a fine value.
And just what is the chance this 60 year old will get a specified disease during this savings period? Pretty darn good. Most people find they can budget for and afford a reasonably price policy to offload this risk. The thing I object to the most if your trivializing the risk of getting Cancer in your "toe fungus" quip. The risk is Very high. I was not kidding about the 1 in 2 men and 1 in 3 women will get cancer before they die. As a family that has been touched by cancer (and most are) it struck me wrong.
I'm not trivializing the risk of cancer. Cancer is a horrible disease and I've seen a lot of people suffer because of it. But it's important to point out that while your chances of getting some type of cancer over your lifetime are high, the chances increase exponentially with age. That means that most people aren't at a significant risk until later in life when they should have had plenty of time to save for an emergency. Also, not all cancers are equally serious. A large majority of the cancers that make up those statistics are basal cell carcinomas or squamous cell carcinomas (skin cancers). As a matter of fact, skin cancer accounts for more cases of cancer than all of the other types combined. It is exceedingly rare for a skin cancer to spread to other parts of the body, the treatment is (relatively) simple, and the prognosis for a skin cancer patient is very good. My neighbor from when I grew up has had skin cancer removed at least a half-dozen times (About all I remember about her from when I was a kid was her laying out in the yard sunning herself constantly). My mother has had thyroid cancer. Neither of them have had costs any different than if they'd have been injured in a minor car accident.
I asked for real numbers that would allow you to demonstrate the value of the policies you're talking about a couple times, but you have conveniently neglected to provide them. That alone should be pretty telling.
You're right. I'm not an "insurance professional." But I am a scientist trained to make logical decisions based on evidence. Personal finance is a hobby of mine, so I also understand how to weigh the cost vs. the benefit of something like this. It would be easier to step out of this and let you "win," but I feel an obligation to make sure that people can see the other side of your pitch and make an informed decision.