I think it's fairly obvious they were going for a paternalistic character in Picard, especially at the start. It's not just his relationship with Wesley, he does the same for Tasha (she even mentions this in her own eulogy), and to some extent Worf and Riker. Even bits of Geordi's dialogue in stuff like Arsenal of Freedom can be interpreted within this dynamic.
The captain of this series was deliberately not the action man of the captain of TOS, but a more diplomatic, thoughtful - and yes, fatherly (albeit crusty) - presence, at least at first. Riker took on the action man aspects of Kirk from TOS. The shift in S2, and esp. from S3 onwards is quite striking, but aspects of the stern father figure remain.