Does long term care insurance usually help pay for sitters?

You will not get more from the long term care insurance. It pays a set amount of money for a set amount of time.

Mom has a pretty common policy written some 25 years ago and I was surprised to learn that it would only pay 60% of her benefit amount as memory care is not nursing home care and the LTC policy covers only a third of the cost for three more years under a 4 year benefit
Her facility is very expensive and we have personal caregivers 12 hours a day as she needs the help which is out of pocket

It depends on what your policy says. My best friend's mom had a policy that paid by $$ amount, so she was in a small facility that cost less and she had money left over for sitters. Read the policy, if you have to get a lawyer to read it.