Whether data scientist need to learn web development or not largely depend on the organization that he or she is working. For larger companies, there are dedicated teams for web development who caters to the deployment of applications to the web; and data scientists are more focussed on delivering relevant models catering to specific business problems.
However, for smaller organizations and start-ups, data scientists may need to learn the basics of web development as they may be required to deploy their applications on the web.
I wont go into the skill sets that different types of data scientists should have, if you one of those you already know this. The one question I would be asking myself is- would adding web development skills be a valuable skill to add to my experience and for me the answer would be yes.
I believe anything we can learn makes us stronger and more valuable in what we do. Understanding what happens in web development would only make you better since you can now understand the overall process.
Knowledge is power and that knowledge will make you more valuable in your business.