Consider what happens in a typical, well-intentioned corporate effort of this kind. It begins with lots of enthusiastic cheerleading at the executive ranks. People are told to dedicate a portion of their time to pursuits that interest them but are not part of their day jobs. Trainers are brought in to teach everyone to be an innovator. There are "innovation boot camps." Ideas come pouring forth from every nook and cranny. Many of them are half-baked and impractical. Others are a poor strategic fit. Others will only tick off supply chain partners or important vendors. Many simply don't have enough upside. And so it goes.
In my experience, most companies have far more innovation ideas than they can ever implement. Most of these won't work out — one study found that a company needed to generate, on average, 3,000 raw ideas to find one that could be a commercial success. The real trouble is that, after all those ideas are generated, the innovation process runs smack into the organization. When I ask participants in my executive programs what gets in the way of growth in their companies, the list goes on and on: lack of incentives, power of the existing business, management desire for near-term success, too many silos, fear of failure, "it's no one's job," and so on. That's the stuff that kills innovation-fueled growth, not a lack of interesting ideas.
So what do companies like Apple and P&G really do? Rather than rely on more-or-less random idea generation, they have made innovation into a systematic process, with dedicated, trained professionals to do it. No company would put a mission-critical function in the hands of people with no experience at making it work, yet it happens all the time with respect to innovation. So encourage your people to bubble away. Just don't be surprised when the bubbles burst upon first contact with your own organizational reality.