I'm a President/CEO of a small company that's growing like a weed. I've delegated effectively and often find myself coming up with a new idea and delegating it. At times I run out of important things to do in my workday. Yes, the free time gives me time to think strategically - but I feel guilty. I don't want to feel guilty, but truly understand that I'm still getting things done, just through others.
Congraluations! If you are able to delegate and find time to be strategic, you ARE doing your jobs. Most startups have trouble getting past their initial success because the founder feels they need to do all the work and make every decision. If you trust your team and can delegate effectively, then you've got a great team and you should focus on vision and strategy.
If you delegate and trust your team to do things, then not only are you happy you get to think strategically, but your team will be more motivated.
I'll add two caveats. I'm assuming that you are developing strategic ideas for your team to implement, and giving them some freedom on how to accomplish your strategy or objective. If you are simply handing out tasks, then micromanaging to make sure they are done your way, then that's not really delegation. That's direction.
Second, if you are constantly coming up with new ideas and asking the team to implement--which pulls them away from the core strategy--then you are in danger of not fulfilling your overall mission no matter how cool each of the new ideas is.
But, if you are focused on the long-term strategy, and working on ideas to get there--and then delegating the work of getting there to your team--awesome.