I strongly believe either pilot should be able to handle a non-normal from the moment it presents itself until the non-normal procedure is completed. This is how we train our pilots both in our training center and when they come to the line. (And saviboy I second CheckAirman’s comments - I hope the mentoring/additional training you provide your FO’s becomes standard at your outfit)
Why do we prefer Captains to handle a non-normal? Why do Captains get paid more than FO’s? It is the intangibles Captains bring to the table - knowledge, experience, wisdom and judgement.
Captains are paid for higher level thinking. In most cases flying the airplane during a non normal is easy, working the radios is easy. The Captain shouldn’t use brain power on those low level tasks. He or she should be using their knowledge, experience, wisdom and judgment gained to be able to think three and four steps ahead to a point where the airplane is successfully recovered.
That’s not to say every FO couldn’t do that, just in most cases the FO doesn’t bring the depth and breadth of those intangibles to the table quite yet - be it experience on the airplane, in the environment, or at the airline.