You just might have to scare her, in a rational sort of way, of course. I'm assuming that she lives alone, and you are THE family. You might also remind her that as a nurse (appeal to vanity) she already knows as much as you know about what can happen in the future. She will get older, she will become ill from time to time, she may have serious injury, and she may become mentally or physically unable to make her own decisions.
Someone is going to have to make medical and financial decisions, and that person will be named sozobe. Unfortunately, the title of "Daughter" carries surprisingly little weight with doctors, hospitals and banks. To act in her best interests, you will need a minimum of Powers of Attorney for financial, medical, mental health, and personal decisions. Believe me, your mother already knows this. This might be a good time to remind her. Trust me on this, Powers of Attorney executed while she is still quite competent in all ways are much cheaper than an uncontested guardianship and conservatorship proceeding. If it is contested, you just ain't gonna believe what it can cost.
It's going to be an uphill battle though, and I don't expect you are going to succeed at this time, and you do risk a certain chance of alienation, especially if she doesn't totally trust your motivations. You might just have to wait till the time she realizes she is having problems, though these things do sneak up on one. On the other hand, if you suspect she is being exploited financially, i can send you a bullet to chew on, so you can get busy right now.
By the way, the New Mexico Office of Guardianship sends out an info packet with all kinds of alternatives to Guardianship and Conservatorship. It is easily the most informative collection of information and resources I've ever seen from either government or a business. You might check for such a thing in Ohio. Possibly NM would would send it out of state, and possibly not.
As for the long term care insurance, it's like any other insurance. You're going to have to make some wild guess about cost/benefit without knowing what will be needed.