Even if "a king could have any woman he wanted", kings were different because men were and are different. Edward IV married for love Elizabeth Woodville, a widow and a mother of two sons who refused to bed him without marriage, but continued to have many affairs also with married women of London merchants. Henry VII married Elizabeth of York to unite royal fractions but there is no information about his affairs.
Henry seems to be like his maternal grandfather Edward IV in it that he wanted to marry for love which was uncommon among royals who usually married other royals for heirs and alliances and then had mistresses for love and/or sex. But Edward IV had many children by Elizabeth Woodville, among them a heir and a spare. And even if he hadn't, he had brothers and they had sons. Henry desperately longer for a son, but he was also unusual in that when he wanted to end his marriage, he had already chosen his next wife among the Queen's ladies-of-waiting (Anne Boleyn, Jane Seymour, Catherine Howard). At least with Anne and Jane, it began as "court love" and his interest became serious after their refusal to bed him. When Henry did make a dynastic marriage with Anne of Cleves, it failed. The marriage with Catherine of Aragon was of course also dynastic, but Henry did know her beforehand.
When a king married a woman without a royal status, that always created envy and discord, also because her relatives were elevated. The marriage of Elizabeth Woodville first alienated Edward IV's cousin, the famous Kingmaker, earl of Warwick and for a time the king had to flee from the country. After Edward IV's death a fateful conflict arose between the Queen (whose brother had raised the heir) and Edward's brother Richard. Also Henry VIII elevated the relatives of Anne Boleyn, Jane Seymour and Catherine Parr, but Anne's fall meant also the fall of his brother. As the uncles of Edward VI, Edward and Thomas Seymour seemed at first fare well, but both were executed.
On the other hand, a foreign Queen can also bring problems, if she too obviously favors her former country's interests or some faction in England, especially if her husband is so weak that she must act for him which was considered improper for a woman (Henry VI's Queen Margaret of Anjou). Although Catherine of Aragon in the beginning of her marriage got Henry to follow his father's advice against England's interests, she was all the time well loved by the English people.
We can't of course know what kind of lover Henry was, but an educated guess is that if a man can easily have women, he don't have a motivation to learn to make love, and of course even women who had known better lovers couldn't be honest about a king's performance. And before all, the Church had strict orders about intercourse: how and when to do it.