TCPA stops discovery once you make the motion. However, you don't just write the words "TCPA motion now, stop discovery plz" on a piece of paper. If you do that, the judge might just decide the TCPA doesn't apply to the case and deny the motion. So, while you are writing your TCPA motion, which you are apparently not allowed to gather and evidence in support of according to this idea, the plaintiff can force lots of discovery while you can't gather anything to help yourself at all.
I'm struggling to even imagine how to implement something like this. Are the defendants only disallowed from starting their own discovery at all if they think there's a potential TCPA motion, or are they also blocked from participating in discovery done by the other side? If the defendants, assuming that the plaintiffs are acting in good faith and the TCPA doesn't apply, do some discovery and find an email saying "Doesn't matter if we don't have a case yet, let's force them to shut up", are they still banned from filing a TCPA motion?