Blood shedding brings forgiveness (Heb.9:22), blood sprinkling brings purification (Heb.9:10). How is Christ’s blood of the New Covenant spiritually applied to us? By sprinkling! (Heb.12:24 and I Peter 1:2). We are purified by his blood, washed, given a new heart as prophesied in Ezekiel 36:24-27.
Even John Gill a Reformed Baptist in his commentary on Heb.12:24 states, “and to the blood of sprinkling: that is, the blood of Christ; so called, either in allusion to the blood of the passover, which was received in a basin, and with a bunch of hyssop was sprinkled upon the lintel and two side posts of the doors of the houses, in which the Israelites were; which being looked upon by Jehovah, he passed over them, and all were safe within, so that the destroyer did not touch them, when the firstborn in Egypt were destroyed, ( Exodus 12:1-49, Heb.11:28 ) which is the case of all such as are sprinkled with the blood of Jesus: or else to the blood of the covenant, sprinkled by Moses on the book, and on all the people, ( Exodus 24:8 ) or to the several sprinklings of blood in the legal sacrifices: and the phrase may denote (it does!-JK) the application of Christ’s blood to his people, for justification, pardon, and cleansing, which is their great mercy and privilege:”
Hence the sacrament reflecting the reality is rightly performed using the same mode!
And it is given to the infant children of believers just as the command to give the Old Covenant sign of circumcision was given to Abraham!