It's not the money. The FAA wants to have no responsibility. If they did, they could have asked to be put on a push-notification for the software that manages their software development. It would have cost nothing to get an e-mail notification. They would have gotten notice that the MCAS parameters had been changed when the status changed to "Approved for released," if not sooner. If Boeing was even more cooperative the FAA would have access to the linked documents showing the internal analysis of the change, but the FAA could have asked if that link wasn't given, also a cheap ask. The FAA doesn't need to be in every meeting, not read every memo - they just need to see what is going to production and that all passes through a document and software vault that can flag significant changes and alert a list of people when they do.
However, with that information they would have done what everyone else did and decide that the outcome of any problem was controllable and now would have that bit of evidence sitting right there when circumstances proved it was not. So they want to avoid ever having any responsibility. As a regulator they can make simple rules like, "Every system must be fail safe." They don't have any obligation to evaluate every system to ensure it is fail safe; just wash their hands of the results and blame the maker for not accomplishing that all-encompassing task.
It still bothers me more that for decades it was acceptable for an ADIRU to lie about the plane being in a stall when it wasn't. The FAA was OK with this. The airlines were OK with this. The maker of the plane was OK with this. And this lie got passed to MCAS. How did that ability to lie get approved? Oh - yes, there is a sink for handwashing in Washington DC. where that lie was deemed not a problem by the regulators.