I read the books as a kid, twice. I was glad they left Tom out of the movies. I mean, what he means to the story and the mythology is STILL being debated, 40 years after I read the books, and that was decades after they had been written. If Jackson had included him in the movies, he would have had to make an interpretation about his nature, one way or the other, or face endless waves of criticism from people (casuals) who don't understand that the character was left vague in the writing. I'm glad he didn't try to nail it down in the medium of film.
The thing is, he didn't need to be in the movies _per se_ --- they just needed to have the Hobbits swallowed up by Old Man Willow, then fade to black, then they awaken on the Barrow w/ a couple of swords, and the ponies tied up nearby, and a figure riding away on a pony humming/singing a tune.
Folks who had read the books would know what had happened, folks who hadn't would just have to accept it as a magical incident/rescue w/o explanation.
Jackson would've had to make an interpretation about his presentation, not about his nature. I see no reason a similar approach to his literary description couldn't be achieved cinematically.
Fwiw I would've cast Tom Waits. And had musical scenes.