The Nephites followed the Law of Moses because it justified their faith in the Messiah who would come to atone for sins.
“Yea, and they did keep the law of Moses; for it was expedient that they should keep the law of Moses as yet, for it was not all fulfilled. But notwithstanding the law of Moses, they did look forward to the coming of Christ, considering that the law of Moses was a type of his coming, and believing that they must keep those outward performances until the time that he should be revealed unto them. Now they did not suppose that salvation came by the law of Moses, but the law of Moses did serve to strengthen their faith in Christ;” NC Alma 14:15
But they always understood the Law of Moses would eventually be fulfilled, and at that point keeping the law would end.
“And now ye have said that salvation cometh by the law of Moses. I say unto you that it is expedient that ye should keep the law of Moses as yet; but I say unto you that the time shall come when it shall no more be expedient to keep the law of Moses.” NC Mosiah 8:1
The Law of Moses ended when Jesus Christ atoned for sin and fulfilled the demands of justice, thereby making mercy possible. Christ told the people at Bountiful:
“I have come to fulfill the law; therefore, it hath an end. Behold, I do not destroy the prophets, for as many as have not been fulfilled in me, verily I say unto you, shall all be fulfilled. And because I said unto you that old things hath passed away, I do not destroy that which hath been spoken concerning things which are to come. For behold, the covenant which I have made with my people is not all fulfilled, but the law which was given unto Moses hath an end in me.” NC 3 Ne. 7:2
This final sacrifice under the Law of Moses fulfilled all the requirements of justice. It created the possibility for infinite mercy: “And that great and last sacrifice will be the Son of God, yea, infinite and eternal. And thus he shall bring salvation to all those who shall believe on his name, this being the intent of this last sacrifice: to bring about the bowels of mercy, which overpowereth justice and bringeth about means unto men that they may have faith unto repentance.” NC Alma 16:34
The Law of Moses was not part of the original faith taught in the Garden of Eden to Adam, and believed by the first fathers. But rather, “the law was added because of transgressions,” (NC Gal. 1:10), which is why it would be fulfilled, come to an end, and it would no longer be expedient for mankind to follow. The process of restoring will not include a return of practicing the Law of Moses. God intends to preach again the Gospel to us, which He also preached to Abraham when he was restored to the covenant: “God … preached before the gospel unto Abraham.” (NC Gal. 1:7) Abraham believed and received the covenant, but did not know or obey the Law of Moses.
There is a great deal left to be restored. But among the many things still to be done, renewing the Law of Moses is not among them.