Theoretically yes. Realistically no. This may ruin it for you idealists, but let me explain why.
If you're on a leadership team, there has to be a point person.
Who makes the decision?
Who takes responsibility for failure?
Who's the leader?
We'd like to believe that leadership can be flat, but that structure doesn't work. How often does indecision, disagreement or different agendas come into play? Sure, the same can be said for the singular leader, but there still needs to be a single person in charge.
At its purest form leadership is about relationships (minus the leverage of position, power or money). One leader works best. Accountability can come from the board or management team, but everyone wants to know who pulls the trigger.
Even in today's contemporary, growing organizations such as Zappos or Facebook, there is still a recognizable face to the brand. Who knows if they are truly the leader, but they're viewed that way.
Instead of thinking horizontal vs. vertical, consider a circle. If a leadership team is placed in a cylinder, it can be turned to different point persons when necessary. A leader doesn't always have to be in charge. In fact, serving and following is an important trait as a leader.
Similar to the saying, "There can't be too many chefs in the kitchen," leadership works more effectively when there is one leader and defined roles for the rest. This isn't about power, position or money, but about bringing the most value to a company by "being on the right seat in the bus."
Yes, leadership skills can be taught, but certain individuals facilitate greater results when they're on top.