Let's look at this verse in a bit of context.
2 Samuel 12:7-8 And Nathan said to David, Thou art the man. Thus saith the LORD God of Israel, I anointed thee king over Israel, and I delivered thee out of the hand of Saul; And I gave thee thy master's house, and thy master's wives into thy bosom, and gave thee the house of Israel and of Judah; and if that had been too little, I would moreover have given unto thee such and such things.
If you carefully read these verses, you will see that it is the wives of David's master, meaning King Saul, that were given unto David by the Lord. That is, when David took over the rule of the kingdom of Israel after the death of Saul, Saul's entire household was available to David. However, there is no record or indication that David ever took any of them to wife. The Lord also told David that He had given to David the house of Israel and the house of Judah. The idea is that he could have chosen wives out of all the land of Judah and Israel.
However, although David has access to the former king's harem and although he had access to any available woman in the entire kingdom, yet he stooped to take another man's wife for his own and then proceeded to murder that man. He is as the rich man who took the poor man's lamb for his dinner--according to the parable Nathan had just told David.
It is true that God allowed bigamy in the Old Testament. In Deuteronomy 21:15, the law makes certain requirements of a man who has "two wives." However, as you point out, it was not His plan from the beginning.
In Matthew 19:4-6, Jesus taught, "Have ye not read, that he which made them at the beginning made them male and female, And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh? Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder."
There was no plan to make three one flesh. That was man's idea. The first example of bigamy in the Bible is with Lamech (Genesis 4:19) who was of the ungodly line of Cain. From the beginning, this practice had bad connections.
Finally, you ask if God would give to man something that was not His original intention for him. Certainly, He will. The Lord wanted the Israelites to enjoy and appreciate the manna that He sent especially for them. However, they continually complained and demanded meat. Finally, God gave them quail to eat--loads and loads of quail (Numbers 11:31-33). However, getting what they lusted for from the Lord brought with it a great cost. A plague killed many people. We should always be careful when we insist on getting only what we want. The beautiful rose of our dreams may have many painful thorns.