There are situations in RPGs where it's entirely beneficial to be the first to act. Sadly most RPGs are pretty poor at running mexian standoffs like the huge mess of people pointing guns at everyone else you see in the poster today. Turn based initiative and metric ass tons of hit points make mexican standoffs impractical and not nearly as tense as a 14 person standoff with automatic weaponry. Unless you're talking near epic level casters in D&D 3.5, who play their own special brand of rocket tag. I admit I used to have an initiative problem in the D&D 4e game I play. Then my rogue passed away and I returned to playing a leader. Our avenger still has an initiative problem. She keeps rolling 2s on her init check. It's a sad state of affairs when the fighter who has an init mod of +1 regularly goes before the avenger who has an init mod of ~+6.
Do you have init problems in your groups? Or perhaps mexican standoff problems?