Because it is practical, prayerful and purificatory so to do.
28. Then the priest, standing at the side of the altar, washes his hands, saying quietly: Wash me, O Lord, from my iniquity and cleanse me from my sin. (“Wash me completely from my iniquity, and cleanse me from my sin.” Ps 51:4).
76. Then the priest washes his hands at the side of the altar, a rite in which the desire for interior purification finds expression.
145. After the prayer In spiritu humilitatis (With humble spirit) or after the incensation, the priest washes his hands standing at the side of the altar and, as the minister pours the water, says quietly, Lava me, Domine (Wash me, O Lord).
|from Saint James Cathedral|
Rite for the Blessing and Sprinkling of Holy Water (p. 1455 GIRM)
Outside Easter Time
Sprinkle me with hyssop, O Lord, and I shall be cleansed; wash me and I shall be whiter than snow. Ps 51 (50): 9. (You can also pray these words, for example, when you dip your finger in the Holy Water font to bless yourself as you enter the nave of the church.)
I will pour clean water upon you, and you will be made clean of all your impurities, and I shall give you a new spirit, says the Lord. Ez 36: 25-26
The liturgical actions of the Roman Rite have their origin in Jewish practice:
And Aaron and his sons shall wash their hands and their feet thereat; when they go into the tent of meeting, they shall wash with water, that they die not; or when they come near to the altar to minister, to cause an offering made by fire to smoke unto the Lord. Exodus 30:19