I can show what happens when you do the opposite (temporarily) on your car... Like 'weakening' the transmission crossmember where the T-bar anchors reside in.
(Removing the tophalf of the crossmember in the driveshaft tunnel to make room for an overdrive transmission.)

Given some time (just a few months in this case), the crossmember started to seperate itself and tear away from the floorboard sheetmetal. This happened on both sides of the transmission near the T-bar anchors.

Only after I fully welded both front and rear sides of the crossmembers to the floorboards this process was stopped.
Ofcourse the real cause, the 'missing' upper tunnelreinforcement, will be fixed to take away the strain on the floorboards.

The car, A-body Dart, has 1" torsionbars by the way.