Why would Apple need to worry about non-Apple users?
Ultimately they could offer the service to them but they may find having Apple Search exclusive to their devices as a positive. It would allow them to offer many unique features such as integrating local and web results seamlessly (amongst many other ideas).
Also, and Apple knows this more than anyone, Apple users are the most capable in their ability to spend money. So although Safari users would be only 20% of the global search market, it's likely the most lucrative 20%.
