Moses made no such alteration. Deut 24 was not Moses' thoughts, he was speaking what God told him to speak. God wrote this Law not Moses. He allowed Israel certain things even though it was not what He wanted for them. Why did He allow it?
Mar 10:4 And they said, Moses suffered to write a bill of divorcement, and to put her away.
Mar 10:5 And Jesus answered and said unto them, For the hardness of your heart he wrote you this precept.
Mar 10:6 But from the beginning of the creation God made them male and female.
Mar 10:7 For this cause shall a man leave his father and mother, and cleave to his wife;
Mar 10:8 And they twain shall be one flesh: so then they are no more twain, but one flesh.
Mar 10:9 What therefore God hath joined together, let not man put asunder.
The people were not given the Holy Spirit and did not have a circumcised heart. What does God say for today?
Act 17:30 And the times of this ignorance God winked at; but now commandeth all men every where to repent:
Doesn't mean God approved, it means God did not pass the ultimate death penalty on them because they have not yet had their opportunity...
Rom 11:7 What then? Israel hath not obtained that which he seeketh for; but the election hath obtained it, and the rest were blinded
When was Israel blinded? It was an ongoing condition from the start...
Heb 3:9 When your fathers tempted me, proved me, and saw my works forty years.
Heb 3:10 Wherefore I was grieved with that generation, and said, They do alway err in their heart; and they have not known my ways.
Notice God was grieved with the generation that came out of Egypt because they did not have the heart to obey God.