There have been numerous solo founder startups funded by YC. Some of them were successful.
I've been making a living doing what you describe (idea -> design&code -> customer support&marketing) on my own for most of my life... I was 14 when I launched my first profitable website, I'm 27 now and support some 100k users myself.
If you're aiming to be a world-changing business, you'll eventually be hiring other people. I'm satisfied dealing with my couple hundred new customers a month, which I can support on my own, and who support my lifestyle.