It seems that is your personal opinion.... but where is this confirmed?
And is such the ONLY, exclusive purpose - there is an impossibility of any other?
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It's not my personal opinion. I still wrestle with the revelation I was given and am willing to admit being mistaken. But it is what common sense seems to point towards. I don't quite understand why a God of reason, love and peace would design the chaotic and irrational actions that precede and accompany the act of human (and animal) procreation. And to call said actions a means of displaying affection seems quite ridiculous to me.
I don't know what you mean by confirmed. Virtually nothing has ever been confirmed to the entire human population.
No, it is not the only exclusive purpose. The passions that accompany sexual intercourse are part of our fallen nature and God tolerates it, just like He tolerates all our other flaws. Sexual intercourse as a means of pleasure within marriage is not (necessarily) a sin, because it has the purpose of helping those who cannot abstain burn with passion. Nevertheless, the more you seek God to free you of these passions, the less power they have over you and the more you see them for what they are.
You can't argue away a reasoned position with an unsupported opinion.
The reasoned position contains logical fallacies.
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Post #1: God did create the reproductive organs for men and women to procreate, but He did not create sex as a means to seek pleasure.
Post #6: Sexual intercourse was designed with the purpose of procreation. Before the fall, God told them to be fruitful and multiply, not to be fruitful, multiply and have sexual intercourse for pleasure.
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Does that mean that someone who cannot bear children for some reason should not get married?
If a partner in a marriage is or becomes infertile, does that mean that the couple should never come together again?
I suggest that some clarifying clarification would help clarify the situation.
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If a person cannot abstain from fornication and burns with desire, (s)he should get married and extinguish his/her passions by engaging in normal (not perverted) sexual intercourse within the covenant of marriage. The husband and the wife should help each other in this sense to the best of their abilities, so that neither of them fall into temptation. (1 Corinthians 7:5, 1 Corinthians 7:9)
Bearing children was initially the main (perhaps sole, but I might be wrong about this) purpose of sexual intercourse. After the fall, everything got twisted and perverted. Without revelation from God, it is impossible to tell the exact details of what is permitted and what is tolerated. We can use Scripture as guidelines.
For example, Jesus says that in the resurrection, humans will neither marry, nor be given in marriage, but will be like the angels. Does this mean that the angels have sexual intercourse without needing the covenant of marriage? Probably not. My guess is that it means that angels don't engage in sexual intercourse. If sexual intercourse is the ultimate form of intimacy, it would be logical for superior beings to engage in it. Should we conclude that angels are inferior to us as far as expressing intimacy to one another is concerned? Most likely no.