Why is it "to have sex" instead of "to sex?"

In the autumn of 1719, after his wife's death, the wealthy Virginia planter William Byrd II visited London, maintaining the diary he had begun years ago back in the Colonies. He dutifully noted the Greek and Hebrew passages he had read every morning, various meals and social engagements — and his numerous sexual encounters, recording each time the number of orgasms:

11 November, went with Lord Orrery to Mrs B-r-t-n where we found two chambermaids that my Lord had ordered to be got for us and I rogered one of them and about 9 o’clock returned again to Will’s where Betty S-t-r-d called on me in a coach and I went with her to a bagnio and rogered her twice, for which God forgive me …

13 … took my ways towards Mrs. Southwell’s but she was from home. Then I walked in the park and went to Ozinda’s … After we went to Will’s … then … to Mistress B-r-t and stayed about an hour

14 … went away to Will’s where a woman called on me … then went to a bagnio where I rogered my woman but once. Her name was Sally Cook. There was a terrible noise in the night like a woman crying. …

22 … walked home and by the way picked up a woman and committed uncleanness with her, for which God forgive me …

Byrd was, by his own account, a very busy man.

To describe these sexual encounters, he uses the verb to roger: Byrd is, of course, the subject; the direct object is the female object of his momentary affection. This is the simple SVO construction you see lacking in Modern English.

Now what D.H. Lawrence called John Thomas in Lady Chatterley's Lover had been called Roger since the sixteenth century, but the verb, still somewhat current in British use, was still new when Byrd rogered his way across London.

Byrd was alone when he wrote his diary, but one can imagine the social context in which he both learned and used the word: with intimate male friends such as Lord Orrery as they reminisced over their sexual conquests.

I would submit that any SVO contruction which depicts the male as active conquering subject and the woman as vanquished direct object arises in just such homosocial contexts and usually stays there: "locker room talk."

Thus the level of taboo or perceived vulgarity when they subject their female objects to their attention is solely up to the men conversing.

In other contexts where it might be permissible to speak of sexual matters, a more mutual expression is far more likely.

We made love for hours on the beach.

John and Marsha finally had sex. It's about time.

The answer to almost all questions about language that start "why" is "because that's how the language is".

Languages happen when people use them. People hardly ever decide "we should say it this way rather than that way, because it makes sense" - or, more accurately, people do say that, but it is very rare that they have any impact on how people speak in general.