There are some instances when a quick arrest is not strategically wise for the prosecution — and that is when the prosecution does not have its case ready for trial and they have a reasonable of certainty that the individual is not likely to commit a crime in the interim period. Speedy trial rights of an accused can kick in (rules vary in each state and the federal system) and that could have impact on the case.
[clarification...I was just told a defendant in Florida can escalate the speedy trial to 60 days....checking on it...but that would mean a bigger reason for a prosecutor to wait until his or her case were ready to try.]
Remember what happened in the OJ Simpson case? The DA pushed for a fast arrest of OJ, and OJ promptly demanded a speedy trial and the prosecution was forced to start trial and the team was far from ready. As a consequence, the trial team spent much of the trial investigating their case (and putting it together) when they should have been focused on actually trying the case.
Of course there is a limit to how much delay is reasonable. A quick, thorough, fair and exhaustive investigation should be done. No prosecutor (or police organization) should drag its feet or hide behind the speedy trial excuse. That is not justice.
(I lifted the Florida speedy trial info above from the website of a Florida lawyer named Eric Matheny. I assume his information is correct.)