I know of a couple where the man divorced his wife in fit of rage and immediately regretted it. They went to multiple muftis and tried to find someone who would "okay" their reunion. But no such luck.
She never remarried but he remarried years later.
I think halala is there as a way to make a man really regret his actions if he gives talaq in haste. Its not just the woman that has to live with the consequences, he does too. If he divorces his wife in anger...he will regret it. No man would want to see his wife with another man. If he loves her deeply enough, he might be alright with a halala. But then emotionally live with the knowledge that she wasnt with him and him only.
If he doesnt go through the halala...at least she is rid of a man that can divorce her at whim and doesnt take marriage seriously.
I think its a matter of perspective.
I think it needs some clarification.
The concept of halala is not proactive 'choice' after talaq has happened.
Meaning, the man is not given a choice of Halala at all to get her back.
Now this petty mch should sum up what is written in Quran about this situation. (Surah Al-Baqar Iyah 230)
It is merely a possibility of remarriage which is allowed and that would only be AFTER the woman get's divorce for a strong reason or she becomes a widower of second husband. And there is another if they stay in limit next time.
So if these two again have some intention to do hanky panky stuff, have some other motive to get remarried, then second marriage is not allowed.
Marrying/divorcing kind of 'bussiness' is not what Allah wanted people to do. Like what happens in Bazaare Husn.
Here is that Iyah:
If a husband [after revoking divorce twice in a marriage bond] divorces his wife [for the third time], he cannot marry her until she has wedded another man. But if this [second husband] also divorces her, it shall be no offence for either of them to return to each other, if they think that they can [now] keep within the limits set by Allah. Such are the bounds of Allah. He makes them plain to men who want to gain knowledge.(230)
In essence: There is no such thing as Halala as a choice in Islam.