Well, you are already getting 6 pulls out of the chase missions. Making it daily would only increase it to 7 pulls. With the amount of fragments ranging between 2-5 and the random nature on which two ninjas are available to choose from makes it very unlikely that you can focus a certain ninja.

Sure, spreading the chases over the week might incentivize daily activity, however it penalizes those who can't login every single day. The chases being centered on the weekend, which for most people tends to be more lax in work/studies scheduling functions just fine.

Just because it works fine doesn't mean it can't be improved. For example it could be an event like team instances that runs from FRI to SUN and you have 6 tries in total for the week, giving the player more choice as to when and if they choose to do them in bulk or stagger them over the weekend.