I don't think it has that much to do with the size of the company though, but more with the difference between a consulting company and a product company.

In a consulting company, work is time-driven: every hour of work is intended to be billed to a customer. This makes the company very focused on time which makes it easier to dedicate X% of that time to individual's projects. In product companies, work is typically much more result-driven, which makes it more difficult to correctly attribute each worked hour of time to any specific activity. As a consequence, it is much more difficult to do these "X% projects" in part because the X is tricky to correctly measure and attribute.