Why should they? They can just prevail on the members to do it - call it service - costs LDS Inc. nothing. I know my mom shuttled handicapped couple who couldn't drive to church for ages and then someone LDS moved into the same apartments and they took over.
Why pay for a cow when you can milk your followers for free?
I have not been impressed with their LDS services in nursing homes. Seems to matter by ward. Some do short versions of RS, Sunday School, and Sacrament meeting. Some can only do a half hour of sacrament meeting and nothing else.
Not lots of tithing $ in the nursing homes anyways. Key is to try and find their next of kin and try and hustle them with the baptism of the dead trip.