In the article linked to the post, it explains that Kaczynski’s lawyers were the ones who wanted it originally removed from its location and preserved.

In an effort to protect it from snoops and vandals, lawyers requested to have the cabin moved from its original site outside of Lincoln, Montana, to a nearby Air Force base.

As the trial approached, the cabin became the focal point of his lawyers’ planned insanity defense. Only a madman, they argued, could have lived in such primitive conditions.

If you think the reason is stupid, sure, but it wasn’t the FBI that made it so important to a potential trial.