If the release of the minutes, instead, came before the next meeting, then market participants would be more likely to react to two sources of information for each single meeting--first to the statement that immediately followed the policy action and then, some weeks later, to the minutes.
The minutes should simply deepen and expand the rationale for a policy decision that was already given in the statement released immediately after the meeting. They might also indicate the existence and strength of contrary views. At the margin, some of this might be additional information.