Feasibility of another product in peroxide effect mechanism of propene
The energy cost of bromine radical abstracting hydrogen from propene is 89 kcal/mole. The gain of forming $\ce{HBr}$ is 18-28 kcal/mol (for a $\ce{H-Br}$ bond from $\ce{H2}$  and $\ce{Br2}$; variation is due to solvent effects) + 23 kcal/mol (from the $\ce{Br2}$ which was fractured into 2 Br radicals by 46 kcal/mol bond energy); so the gain is 41-51 kcal/mol vs a cost of 89, or a net cost (net energy requirement) of 38-48 kcal/mol. This would be a slow reaction with an activation energy even higher than 41-51 kcal/mol. (All data from CRC Handbook)

The alternate reaction, of adding a Br radical (with 23 kcal/mol energy above ground state) to propene, loses the pi bond and its energy (84 kcal/mol) and gains a $\ce{C-Br}$ bond (70 kcal/mol). The energy cost of forming the bromoradical is 84 but the gain is 70 kcal/mol for $\ce{C-Br}$ plus the 23 kcal/mol from the Br radical, or 93 kcal/mol. Net gain is 9 kcal/mol. This reaction will go spontaneously while the first will not (rate determined by activation energies, of course). 

It turns out that allylic stabilization is only part of the story, and is, in fact, rather small: the bond strength of $\ce{H - allyl}$ is 89 kcal/mol vs the bond strength of $\ce{H - n-propyl}$ which is 98 kcal/mol.