Trump just took advantage of what was already going on. He simply recognized what many of us warned of. When the tea party became an "organization" it took on leaders who could be bought. The tea party express became nothing more than a means of funding itself by hiding behind a few conservative speakers while inviting establishment politicians to come and speak and that was before Trump came along.
Anyone who really remembers the beginnings of the tea party remembers the strongly anti politician stance that we didn't want to hear from politicians. They were to shut up and listen to us.
One of the major fallacies of the early tea party movement was that it could effect political change without participating fully in the political process. Without national leaders and without a broad organization (and I recall being told in no uncertain terms that the tea party movement needed neither) such a movement is mainly talk, simply through
lack of organization.
There were a few politicians who were elected on explicitly tea party principles, and the FC is apparently all that remains of them.
Still, while you're probably correct about the failings of the "tea party express," you're not correct that Trump took advantage of the "leaders." Instead, he took advantage of the underlying anger and frustration that has informed the Tea Party movement since its inception. That he probably didn't mean it was obvious to a lot of us -- it's what demagogues do.