Joseph Fielding Smith says that washing and anointing by women should not be encouraged.
Joseph Fielding Smith, Letter, July 29, 1946, CR 11 304, Church History Library
While the Authorities of the Church have ruled that it is permissible, under certain conditions and with the approval of the Priesthood, for sisters to wash and anoint other sisters, yet they feel that it is far better for us to follow the plan the Lord has given us and send for the Elders of the Church to come and administer to the sick and afflicted.
The service of washing and anointing is not a Relief Society function, and, therefore, is not under the direction of the Relief Society. Women should not be set apart to perform this ordinance, but the presiding Priesthood authorities may determine if such an ordinance is to be performed and designate the sisters to perform it. The washing and anointing by our sisters in the past was greatly abused and improperly done, and for this reason, as well as for the reason that the Lord has given us by revelation the order for the administration for those who are sick or in need of a blessing, the washing and anointing by the sisters has not been encouraged.