The official answers are recorded on wikipedia are likely true. specifically, most of the directors felt Bombadil would confuse the audience and perhaps set the screenplay storytelling back.

It would be like if you knew that that a) The Japanese ambassadors delivered the declaration of war to the USA two days before pearl harbor. b) they picked up the approaching japanese aircraft on radar and did not sound the alarm. a+b = means you dont have to explain the true geo politics behind WWII and that it was baked in the cake. Then you can demonize an incredibly honorable people like the japanese. Or, if you figured out just a) or b) you can blame it on just the subterfuge or incompetence of just that compartmentalized set of actors.

If the Bombadil story was included, they'd have to explain that the council did not chose him to carry the ring or be part of the party. mess with story in regard to the hero's shown, and the failed heros.

In this metaphor, Tolkienverse Tom Bombadil joining the fellowship would probably have been like the USA's role in WWII. But in How could you explain the reality world today if the USA did not get involved?