Neither Tom nor Sonny were "built for it."

I believe that Vito recognized Sonny's shortcomings long ago, and groomed Tom to compensate for them (making Tom overly cautious and conciliatory in contrast to Sonny's hotheadedness and inclination to violence). Vito planned to have them succeed him as a team.

I believe that Vito realized after his return from the hospital that the plan was not working, but hoped S & T could hold things together long enough for Vito to recover and bring Michael into the fold to support Sonny and Tom.

Sonny's death made this impossible, forcing Vito to get better fast, end the war, and accelerate the process of bringing Michael home.