As it stands it is way too easy to use as a weapon to sue people into submission. Although I think this is already well known.
But consider this: To be fair to plaintiffs, the bar for "not frivolous" would have to be fairly low. I suspect that a fair pre-vetting system would only weed out a tiny fraction of lawsuits. Probably, even most lawsuits that end with a successful motion to dismiss would make it past the type of preliminary review by the court that you're proposing.
So it's a good idea, but I think something more would be needed to help protect the little gal/guy from legal bullying. (BTW, I'm not saying this particular case is an instance of legal bullying. We only have one party's perspective.)
The legal system would benefit greatly from being framed as a cost/benefit optimization problem instead of as reasoning in a byzantine para-consistent logic.