Where did you find the implication that the League Militia or navy underperform on the initiative? I do not see it.
Ask yourself this: How did a non-state actor take control of nearly the entire FWL fleet?
Why has the FWL consistently lost worlds to a nation that trains better officers for the mercenary market, their national rivals, everyone, that is, except themselves?
When your two major borders are the CapCon (crippled by top-down organization and economically hampred) and the Lyrans (who tend to train great officers for people who are NOT Lyrans, while keeping the worst they can turn out)?
In the first instance, nobody bothered to ask what those cannisters were or why they were being brought aboard. Nobody
took the initiative to question it.
in the second case, Initiative isn't merely acting, it's knowning WHEN to act, and what to do. In intensely politicized environments (and you can't tell me the FWL doesn't qualify there) the typical reaction is to withold information and keep your head down, while sabotaging anyone who looks like his success is going to impact yours.
Nearly every modern military claims to prize initiative, but there's a significant difference between what's on the letterhead, nd what's in the actions.