We propose a model for the abrupt emergence, below temperatures close to the glass transition, of the ultra-fast (GC) steady mode of spherulitic crystal growth in deeply undercooled liquids. We interpret this phenomenon as controlled by the interplay between the generation of stresses by crystallization and their partial release by flow in the surrounding amorphous visco-elastic matrix. Our model is consistent with both the observed ratios ($\sim10^4$) of fast-to-slow velocities and the fact that fast growth emerges close to the glass transition. It leads us to conclude that the existence of a fast growth regime requires both (i) a high fragility of the glassformer; (ii) the fine sub-structure specific of spherulites. It finally predicts that the transition is hysteretic, thus allowing for an independent experimental test.