Numbers 3:41-45 did not nullify the redemption price of the firstborns. It only expressed God's taking of the Levi tribe instead of the firstborns of every tribe to be ministers in the services of the Lord's tabernacle.
It was stated later in Numbers 18
14 “Everything in Israel that is devoted b to the Lord is yours. 15The first offspring of every womb, both human and animal, that is offered to the Lord is yours. But you must redeem every firstborn son and every firstborn male of unclean animals. 16When they are a month old, you must redeem them at the redemption price set at five shekels of silver, according to the sanctuary shekel, which weighs twenty gerahs.
So why does Nehemiah require that the firstborn be brought before the Lord?
To resume the usual practice of collecting the redemption money by counting the number of firstborns being present. It was a special event. Before the exile, the people brought their firstborn babies at one month of age.
34“We—the priests, the Levites and the people—have cast lots to determine when each of our families is to bring to the house of our God at set times each year a contribution of wood to burn on the altar of the Lord our God, as it is written in the Law.
35“We also assume responsibility for bringing to the house of the Lord each year the firstfruits of our crops and of every fruit tree.
36“As it is also written in the Law, we will bring the firstborn of our sons and of our cattle, of our herds and of our flocks to the house of our God, to the priests ministering there.
Basically Nehemiah was setting up the initial process of financing the continual upkeep of the rebuilt temple as he talked about tithes and storerooms further on.
37“Moreover, we will bring to the storerooms of the house of our God, to the priests, the first of our ground meal, of our grain offerings, of the fruit of all our trees and of our new wine and olive oil. And we will bring a tithe of our crops to the Levites, for it is the Levites who collect the tithes in all the towns where we work. 38A priest descended from Aaron is to accompany the Levites when they receive the tithes, and the Levites are to bring a tenth of the tithes up to the house of our God, to the storerooms of the treasury. 39The people of Israel, including the Levites, are to bring their contributions of grain, new wine and olive oil to the storerooms, where the articles for the sanctuary and for the ministering priests, the gatekeepers and the musicians are also kept.
“We will not neglect the house of our God.”
Nehemiah was concerned about the income collections for the rebuilt temple when he called the firstborns to show up.