You're right, it may lead to "somewhat" more rigidity. Like as in pretty much imperceptible. For those who've actually looked at the structure of the shock tower and firewall system/castings on the ST, you'll see what I mean. None of the braces I've seen will have any measurable effect on left-to-right or front-to-rear torsional rigidity. In simpler words, as you corner,due to to the loading of the suspension, you impart a twisting motion from left to right (one shock tower tries to move up the other down). That design won't limit that.
The other force to consider is where one shock tower wants to move backward and the other forward (like cornering under braking or acceleration). It won't address that situation either.
As designed, it will only help inhibit the shock towers from moving toward each other (compression- both wheels hitting a giant pothole simultaneously) or moving away from each other (tension- both wheels leaving the ground simultaneously). I don't see where it will make any difference in "improved response" or "better handling".
It does look nice underhood though.