Victoria Gardens were once surrounded with low metal railings. These could be easily stepped over, so I'm not sure if this well-trodden path between the University and Church Street predates their removal or not. While still there they at least gave out a subliminal message to respect the grass. This may have helped but now the scarring only disappears in the most favourable of growing conditions. The cold and lack of rain certainly seem to be hindering recovery at the moment.
It would be a shame to lose any of the grass to permanent paving, and the consequent diagonal bisection of the Garden would not be attractive. Perhaps the solution should be aimed at making it less energy efficient for walkers to choose the direct route. This would spread out the footfall and in damp conditions even persuade some to follow the perimeter paving. This might be achieved by positioning narrow shrub beds for several yards along the edges of the garden at Church Street and the University, and a strategically place bed or landscaped mound near the centre of the garden.