Starting a new web designing business is still viable because it is now easier to host your own websites and that web design tools are getting better. There are still certain people or companies who want to have their own websites but are lazy or not able to do it well. Thus, this is a very good chance for you to set your target customers and use your web design expertise to cater to their needs, for example customising for them rather than providing a 1-size-fits-all. Bottomline here is just go ahead!