You're not likely to need this 'til well past 50, so you're not "late".
Yes, you'll pay more if you wait . . . but if you start it early, you'll pay for more years. You can't win in the insurance game.
We have long-term insurance on me, but not on my husband. That might sound foolish, but I think it's the right choice. I'm younger than he is, I'm in better health, and if genetics count for anything, I'll probably outlive him by about 30 years. In short, the likelihood is that he'll have me to take care of him . . . but I'd have to count on our children, and I don't want to place a financial burden on them. They may end up taking care of me, but I don't want them to have to squeeze me into a too-small house or make financial sacrafices to do so.
Also, be sure of what your policy entails. I'm sure you want a policy that'll allow you to stay in your own home and pay for help -- maybe occasional help at first, then more as time goes on.