Alphabet CEO Larry Page was in recent discussions to hire Carl Bass, CEO of Autodesk, to lead Andy Rubin’s former robotics unit, say people briefed on the discussions. The appointment would have ended an almost year-long search for a leader to wrangle Alphabet’s messy group of robotics startups.

But the discussions fell through for a mix of reasons, including how much control Mr. Bass would have over the unit. The episode highlights a big question hanging over Alphabet: Will the structure of the company allow Mr. Page to recruit the best talent to start up new companies or take over one of the existing ones?