You pretty much need "fast track" in order to get any negotiated treaty passed, because you can't have a finished treaty be amended by congress, since that would require that version to be resubmitted back to the treaty partners for approval.
That said, it doesn't remove the Constitutional necessity of having a 2/3 majority to approve them.
Calling them "trade agreements" to get around the 2/3 requirements rather than simply having up/down votes on them as treaties is dishonest. Of course anyone who looks for honesty from our government is a fool who will ultimately be disappointed. Our feral government will do what it wants, when it wants to get what will most quickly enrich the oligarchy.
I think Cruz would have done better to have fought this from the perspective of this undermining of Constitutional authority. That would put him clearly on the side of supporting a 'fast track' provision for treaty negotiations, while at the same time opposing this particular legislation because it undermines the Constitution and the Senate's advice and consent powers/requirements.