I can tell you it will shake your teeth out if it does break or come loose. I was going down the interstate doing about 65 mph in my 1950 Ford in about 1970. I heard something hit the floor board and then all H%&& broke loose. One of the retainer clips on the front U joint came out and then the cap came out so there is like 1/4" play in the joint. It flopped around and then came apart. The emergency brake cables were the only thing that saved me. The driveshaft flopping around under there broke the cast iron tail shaft on the 3 speed transmission. It shook the car so hard it popped the hood latch but safe catch caught it. It blurred my vision it shook the car so violently.
The plate your mechanic is talking about is pretty beefy, 3/16" thick maybe with 6 I believe 5/16" bolts holding it up to the floor. It would sure help.
In the 60's before they required the safety loop on race cars a friend of mine flipped his car end over end three times and he woke up in the hospital. Front came loose and shaft stuck in asphalt and pole vaulted the car into the air probably doing 80 mph on a circle track.
I am putting a loop on my 72 Q vert along with a 6 point roll bar since I will be on road coarse and drag strip with it. Will also have a scatter shield over the flex plate torque converter. I have seen flywheels come through the floor, dash and out the windshield. Also cut the steering column and headers into. He was lucky did not loose a leg or foot. It was a new bone stock 289 K code at the Asheville drag strip.
If you ever have one come loose or break you will remember it.
The pictures are of a parts car I was tearing down. Exhaust was also tucked in the tunnel and PO had put to spacers under the plate to clear the pypes exhaust system. Does not show all but you can see partial.
David