This article along with several comments do a fine job of illustrating why it is the place of a priest and only a priest who may administer this Sacrament.
There has been some speculation that this may change in the future, but I don’t think it is being discussed by anyone who can make such a change.
Viaticum, (the last Eucharist for the journey) is something else.
Anointing may very often include viaticum for those who can take food, but viaticum does not need to include Anointing.
Those Deacons in hospital or hospice ministry have done so any number of times without being aware that it is the faithful’s last reception. In that sense, many lay persons have done the same.
But as an ordinary minister of communion, it could fall into the Deacon’s role should it be requested. However, if there is time, a priest should administer viaticum as annointing can then be done.
Why can’t deacons confer Anointing of the Sick?Deacons can baptize and they can witness marriages, they can even distribute communion as an ordinary minister, and yet the Church does not allow deacons (nor any who are not priests) to confer the sacrament of Anointing of the Sick.A brief consideration of this question – Why can’t a deacon confer Anointing of the Sick? – will teach us a great deal about this sacrament. Read More: