Free will, as we understand it, is not a thing that exists in Tolkien’s universe.
It is true, the Ainur love the Children of Iluvatar because of they are “strange and free”. However, this description interestingly follows shortly after Tolkien writes that the Ainur “know much of what was, and is, and is to come… Yet some things there are that they cannot see… for to none but himself has Ilúvatar revealed all that he has in store…”. The Ainur may not know all that will happen, but this is only due to their imperfect knowledge of the Music; Ilúvatar, on the other hand, has already determined the play that is to come, that of life in the World. Thus we have two conflicting accounts, one of two races loved for their ability to exercise free will, and the other of a World whose history is written in advance.
We can reconcile this conundrum by reflecting on the Ainur might understand being “free” to be. For the Ainur, and especially the Valar, life must be a rather boring affair. It would be akin to watching a movie only after reading an extremely detailed synopsis of the film on Wikipedia—we can appreciate the story, the directing, the acting, the costuming, but the main dramatic effect is gone. We know how this ends. We know that after Luke falls down an airshaft, Darth Vader will lean over and rasp out, “I am your father”, and then Luke will scream and make a crazy face. It’s entertaining, on some level, especially if you haven’t seen it in a while, but not suspenseful, not dangerous, not free. Luke will always fall down, Darth Vader will always say those words, and Luke will always scream. Likewise, Melkor will always rebel, Beren will always fall in love with Lúthien, and Lalaith will always die of a pestilence. Valar know the story of the World. They know the fate of the Quendi. Men are a little more mysterious, but not by much.
Given this, I can almost imagine Manwë being pleasantly surprised when he finds that Melkor has been secretly building Utumno: “Oh, interesting, I literally did not see that coming. That’s a nice change from the usual. That really throws an unexpected kink into things! Although it does make sense, since I do know that eventually we’re going to chain him up.” Obviously, it’s impossible to know exactly what each of the Valar knows or does not know, and it could be that enough of the everyday trivialities of life are outside of their precognizance to make life interesting to some degree. But imagine if you knew, in broad brush strokes, the major events of your life, and of those around you, and of your family. Suddenly life becomes a trial of going through the motions, of fulfilling stories you know are coming.
From this point of view, the description of the Children of Ilúvatar as being “free” is more understandable. They are free, in a sense, in a way that the Valar are not. Elves and Men do not know that is coming. The future for them is mysterious, shrouded in mists. It is true that Elves have some gift of foresight, but only if they choose to use it—in other words, they can read a little ahead in the Wikipedia synopsis, but only if they want to. In Tolkien’s universe, free will means only to act without knowing that every action is predetermined, even though this is in fact the case.
In light of our new definition of free will, how can we approach the drowning of Númenor, that event which seems to cause the Valar such grief? When Manwë sends messengers to the Númenóreans in an attempt to reassure them of the rightness of their ban from Aman, the Men ask of the immortals: “Why should we not envy the Valar…? For of us is required a blind trust, and a hope without assurance, knowing not what lies before us in a little while…”. Here we see that not only are Men envious of the immortality of Elves and the Valar, but also of their gift of foreknowledge. It is hard, the Númenóreans say, to meander sightlessly about the world, not knowing if one’s choice to marry X was correct, or if one should have married Y instead. “Should I have moved to Eldalondë? Perhaps my business would have done better if I had stayed in Rómenna…” etcetera, etcetera.
According to our earlier conclusion that the Valar might in fact envy the Children of Ilúvatar their lack of foresight, this unknowing walk into the future must seem downright pleasurable to those who have seen the history of the World unfold. In fact, the Valar in some respects get to share in Men’s experience of blindness, as they say in response to the above question: “Indeed the mind of Ilúvatar concerning you is not known to the Valar…”. Of all of the Music that was sung before the creation of the World, it is uniquely Men (although Dwarves too seem to be outside of the Music, perhaps?) in whose making the Valar had no part; they are only of Ilúvatar’s will, and his Gift to them is therefore not understood by the Ainur. For beings who spend literally thousands, if not millions, of years simply waiting for a story they already know to unfold, the excitement of not knowing Men’s narrative (at least in its particulars, for they must be able to see some of the general motifs from the large events involving other races that they do know) would be the most entertainment they have had in a very long time. Especially in the story of Akallabêth, when Men are behaving so irrationally and therefore unpredictably, we can imagine the Valar sitting around at a garden party in Lórien, animatedly discussing what those Númenóreans will do next. The drowning of Anadûnê was indeed inevitable, as it was woven into the Music by Eru, but perhaps in the context of Arda, where all is predecided, the rebellion of the Men of Númenor was about as free as it gets.