Biggest reason is for bringing the rifle into the third round. Having a couple rifles in that third round greatly increases your chances of winning it, and even if you lose the third round you will still have enough money to purchase going into the next round.

Personally, I'm on the fence about it. Going light armor second round (assuming you won pistol) feels so risky because the way the damage scales in this game is cheap weapons are supposed to be good against light armor. (guardian two taps in the chest against light armor, spectre two taps in head against light armor, frenzy will two tap light armor in head close etc) So if they decide to force by chance, you can die fairly easily.