They are neither art nor design. Startups are businesses. And a business exists to profit. Nothing else.
Also, a startup does not aim to solve a problem in an industry. That is a common but rather poor approach. A startup aims to profit by filling a need in a given marketplace. Two different things altogether.
The basis of a product is design. But design is not art. Design is engineering. Even UI design, a process commonly thought of as artistic. That is where I disagree with your point. I don't reason anything in a startup is about art.
The difference about solving a problem and filling a need is pretty simple. You don't profit by solving a problem. You profit by filling a need.
Problems inside industries may not have profits hidden inside. But needs, everyone always has money to solve their needs. Your job is to find those needs and engineer a product that fills it.
Edit
--Added this part from my workstation. The text above was from my phone (makes it harder to type in detail).--
Everyone will always have problems. You solve one, two more pop up. The very nature of problems make people be wary of any solution that aims to solve them. And to be frank, a lot of people dont even want to solve their problems. Businesses also share this.
Now needs. Well needs are something entirely different. Needs are wants. What people want, they pay to get. Your job in a business is to find those needs, and give the need what it wants. In software, a need may be to save them money on their accounting. Why is this a need? Maybe the business owner wants to buy a new car, and he/she needs the money to get that new car. There is no problem to solve. Their accounting might not need to be solved. But the owner has a need for money to buy the car.
Typing in my phone is frustrating. I end up writing differently. It makes me compress ideas into short sentences to avoid the pain of writing with the poor UI.
It may seemed like I was trying to debate your point, but I agreed from the start. Now that my hands are free to do so, I wanted to let you know.
Would you be willing to expand your original post? It was rather short in nature.
Also, mind sharing an email? Mine is on my profile.
Also, a startup does not aim to solve a problem in an industry. That is a common but rather poor approach. A startup aims to profit by filling a need in a given marketplace. Two different things altogether.