The audience may have been interested by the Barrow Wights but them and Farmer Maggot and especially the momentum stopping Tom Bombadil were entirely unnecessary for the film. A shortcut to mushroom functions very well in the film. It has elements from the books to make it recognizable, but it keeps the pace up and heightens it and it sets up the rider as a genuinely scary presence. There are more than one way to skin a cat and Tolkien's first third of FOTR meanders entirely too much for a three hour film. Things needed to be dropped, condensed, altered, and shifted to make the film function like a film and less like a nature hike of the greater Shire. It's fine to love Tolkien's work, we all do, but these are adaptations and films and what works in the books doesn't always make for good cinema. Things have to be altered.
I'm not saying Jackson's way is the only way or the best way, but another director would have made changes as well and cut stuff. I doubt any director would include Tom Bombadil. It's just not realistic or reasonable to want the films to include characters or scenes that have zero bearing on the greater plot.
Well, I see why you picked your name oh evil one
We can disagree on this. I can absolutely see a more faithful telling of the parts in question not being too slow. Here's how I see it:
Rescued from Old Man Willow by Bombadil
A respite and advice from him
Leaving his house and getting caught by the Barrow-wights
Their rescue and safe passage to Bree
There are several instances of similar situations on the quest (probably the most notable being Rivendell and Lothlorien, but there are others).
The only difference with Iarwain Ben-adar (Bombadil) is that he isn't really well defined in the Tolkien mythology (It may be that he was pulled in there by JRR himself without really being part of the fully fleshed out history of middle earth). There have been suggestions that he is of the Maiar, Valar, Eru Iluvatar himself, etc., but he doesn't seem to fit into any of these molds. My take is that he may be the embodiment of Middle-earth and its creation itself.
Gandalf himself said at the Counsel of Elrond that he thought that if all else was conquered, that Bombadil himself would fall last (as he was the first).
THE most interesting aspect of Bombadil is that he was TOTALLY unaffected by the ring. If it had been left with him, he would have forgotten about it or lost it as it would have no hold on his mind. So, not a Maiar (as were Saruman and Gandalf) or even a Vala. Eru Iluvatar??? Highly unlikely.
My take is that Bombadil was unique and could have been a very interesting character. On top of that, I don't believe FotR needed to be compressed the way in which it was. It could have been longer and more inclusive. If it took 4 or 5 hours, fine. Edit it and break it up into 2 films (PJ is GREAT at that) to be shown maybe 4 or 5 months apart. I'm not saying the time frames are a blueprint, but something could have been worked out and I think people would have enjoyed it.