That's a very popular question nowadays. I would say, it depends on your niche. In some niches, it's enough to use social networks to promote your business. But, some businesses can't get a lot from social media. The problem for most companies who wanna get more from social medias is that the manager or the owner of the business don't have a clear understanding of its targeted audience.
If you want to use only social medias, you need to have a clear vision about each social platform you are using and know what audience is "sitting" there.
Social medias are growing fast, and we can see how, let's say, Facebook gave people a chance to open their shops inside Facebook groups (pages), where you can sell products directly from the Facebook.
I think it's only the beginning of "socialmedialisation" of businesses who are working online.
So, you need to know what you are selling and to whom you are selling. You may thing that that are too straightforward things, and it's easy to understand who you are selling to, but believe me, there are much more clients that you can get from the internet if you take a week for researching your audience.
Sorry, for the long introduction, now I will explain why you need to know it and how this knowledge can help you decide to use your own website, or you can sell via social media.
1) Know what you sell
There might be a situation that you are selling some soft, and there is no other way to show how good you are in programming whether to show your potential clients samples of your works. There will be a massive problem to upload your samples inside social medias. The best way to do it is to share the link to your website, where people can find you examples.
So be sure what you sell.
2) Know who you are selling to
As you may know, all the social medias have some specific audience. If you know your audience, you can decide which social media suits your needs. As an example, you are a designer of clothes; your audience middle age is 27. Now you know that you need to find the social media using the "age criteria" and Facebook is not the only one social platform that you can use for your online marketing needs. You can search for more different platforms, which are more specific for the product you sell and have an audience who may search for your product inside this social media.
If none of the social platforms suit your needs, the only way to promote yourself or your company is using your own website. But you need to have knowledge in such fields as SEO, Content Marketing, Digital Marketing, Inbound Marketing or other areas that help you to promote your website on the internet.
I would recommend learning Inbound Marketing, coz I think it's the most useful part of internet marketing that can help you power up your skills and succeed!
According to everything mentioned above, it's your right to choose using the website or not.