Of course, as long as there are customers using IE 11 that provide a significant benefit your business — you support IE 11.
But today you have the choice to push for a world without IE 11 (Today IE has ~2% market share). By forcing your clients to use a modern browser you are making the life better for your clients. They will have to move to a modern browser sooner or later. Yes it may be uncomfortable for your clients in the short term / in the long term they will benefit more from the modern browser.
Even Microsoft does not want you to use IE.
Microsoft Edge Chromium will get a Internet Explorer Mode — to limit the users leaving a modern browser to use IE. Giving Admins tools to restrict the usage of IE.
Quote from the security chief: IE is a compatibility solution / not a browser
Microsoft security chief: IE is not a browser, so stop using it as your default | ZDNet
Is Internet Explorer (IE) a browser? According to Microsoft, no. Today, it's a 'compatibility solution' for enterprise…
It is part of the job of the developer to educate non developers. You need to communicate benefits / downsides of your solution. Managers, Business Analysts, Clients need to be able to make an informed decision. They do not follow the news about browsers — they rely on you to tell them about options, trends and risks — in words that they understand.