There's nothing wrong with taking advantage of 0% offers. I've got three cards w balances right now on 0%. But yes, even having small balances report on your statements will have a negative impact on your score. So if you want to app for new cards and put yourself in the best possible position for approval and decent CLs, the better strategy imo would be to pay as many of your cards to report zero. You can't have it both ways - take advantage of a bunch of 0% AND get approved for new prime reward CCs w high CLs.

Gardening since 7/16/14
Current:
EQ 711 7/13/14;
EX 724 TU 721 6/19/14
Goal: 760+