The largest reason today is protecting your standard of living.
In cases where you were to be covered under a governmental system you would not be able to assure where your care would be given, whether you could avoid being in a semi-private room, or even where your facility would be geographically. A private long term care policy puts all of those decisions back to you and your loved ones. Also, many facilities are becoming strictly private pay - so without a policy such as this or the out-of-pocket resources you may not have been able to enter facilities that you otherwise would have chosen.
Another reason is avoiding the dependence that an illness or injury inadvertently places on loved ones. Families often pull together in times of hardship, but the toll of fulltime care giving is rarely understood until weeks or months into the event. Informal care giving by family, while common, is a difficult task over long periods, and caregivers simply become worn down to the degree of becoming ill themselves or more prone to injuries due to fatigue or repetitive motion activities. Additionally, there is the financial stressor of lost income, or juggling the priorities and needs of the caregiver's 'prior life,' with the 'care giving life'.
Long Term Care Insurance should not be seen as a replacement for a loving family however, it should support the caregiver. If a child or spouse wishes to take on the majority of care giving, a good policy will support that wish and only take on the roles the family needs assistance with. It can also help the family find good caregivers in their community and make home modifications like widening doorways or converting stairs to a ramp for a wheelchair. Some care givers would prefer to be excused from some events that are more sensitive, such as bathing or using the restroom. If the family caregiver needs more help, they can in turn lean more and more heavily on the policy so that there is always a 'Plan B' in case it's needed. In some cases family, unfortunately, cannot spare the second income potentially lost by the potential caregiver, and again the policy can take charge of the situation so that you are never without a way to make a situation work to the best of all concerned.
The third largest reason would be the protection of your assets. Faced with a potential of spending down the assets you've put away over a lifetime is simply overwhelming for most people. With a long term care policy you can pay a fraction of the cost you would have been otherwise faced with and build a 'firewal' of sorts around your savings, investments and 401K so they can work as intended and not be prematurely depleted.
For additonal information about long term care insurance, click on the link below.
Download Long Term Care Insurance Educational Guide