Obviously everyone is different. Some use their player, some house, basic low end, fancy, heavy, forward weighted, special tip etc. If you are happy enough with a house break then you can save the money, but you will have variations in tip, weight, balance and feel which may throw you off some. Having your own cheap breaker may not drastically change or improve your break, but the consistency alone can possibly help improve the break plus any tweaks like the tip. And as a bonus you know exactly where that cue has been.
Playing league and such, I have a 4x8 case that carries all my stuff. I have a Black Ice break cue which I love. When I am hanging at the smaller bars I started taking just the player in a 1x1. It is much less obtrusive and cumbersome, but this means I have to break from the wall. For me I do see a difference in my break, so now I am planning on getting a 2x3 so I can carry my breaker too. My friend always just used a cue off the wall to break and gets great action tried my breaker a few weeks back and has been asking me to use it to break now.