Picard can be very intimidating if he wants. Witness the scene in "Lower Decks" when he gives Ensign Sito a very stern dressing down down for something she did in her past. Also as the Klingon Arbiter of Succession he can curse with the best of them.
Picard lets Riker and Troi handle whatever issues his crew might have, since he might look a little unapproachable to the regular crew. He is certainly the most "serious" of the five captains we have gotten to know over the years.