Is initiative just used to determine the first hit? I think combat is based on a series of rounds, in which case it should effect attack speed, recovery time from interrupted attacks, etc. Maybe one of the Larians can comment on this.
Try boosting survival and speed and see if it helps with the relative attack rates. Your trophy list will have details on their stats, that should help you figure out why skeletons are faster. If you have found a lot of armour, each piece may have a small negative effect on initiative or speed.
If you move your cursor over a primary stat, it will tell you what it effects. Speed helps with initiative and evasion; survival helps with initiative and a couple other things. In the demo, when I hit level 2 I boosted survival and speed to 3 (starting with a warrior stat distribution, strength got raised to 6, everything else was raised to or stayed at 3). The next couple levels I think I boosted survival and speed by 1 each time, and did not notice skeletons having a faster hit rate (though there were only a couple in the demo).
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