I say yes and no. There are millions of pages out there working fine without a special design.
Pages people made for themselves, friends and their family. As long as THEY like the look they can call it their own design. What you and I think about their pages does not matter.

Thats because each person on this earth has their own opinion about how things should be and look like. You cant find two of the kind and therefore it will be just as many designs as it is living persons creating pages on the web. So it is, and so it will be.

You can of course change a persons first natural feeling in many different ways, good or bad. A good one is education. It could be about anything, and Im sure you are an expert in some area that gives you more feelings then others who knows less in that subject.

Take wine. A beginner knows nothing, all wine taste almost the same. After a while testing and some study in the subject, they will find big differences in the taste.

The bad ones, is bad influence or pressure from other peoples opinions.

Dont ever buy a design that you dont like to 100% because the Agency say it best for your business. They only say so because they cant deliver what you really like as they dont have the right skills or education to do so.

As we all have our brains in a left and right part, some people (strong left) does not have the ability to find ideas for their web design and need help from an agency.

(The concept of right brain and left brain thinking is developed from an American psycho-biologist Roger. W. Sperry. He discovered that the human brain has two very different ways of thinking. The right brain is visual and processes information in an intuitive and simultaneous way, looking first at the whole picture then the details. The left brain is verbal and processes information in an analytical and sequential way, looking first at the pieces then putting them together to get the whole.)

An artist or designer (strong right) can actually see the painting or the design on the white canvas long before they start painting. On the other hand, they have so many options to choose from, so they need a lot of input from their client to find out what he would like to see when all parts come together as a website.