I think that really depends on your situation and how necessary you find it to appear professional. If you're just doing the webcomic as a hobby or are just starting out, you probably won't need it. Conversely, if you tap into Tapas' audience and become really popular here and/or publish through them, you also won't need your own website.
Building a website is a time investiture. To make one, you either need to: find a template, build it yourself, or hire someone. Even finding a template, you should probably know enough code or website design to be able to customize it. Then, because your website doesn't have an in built audience, you have to market the crap out of it yourself and make sure the SEO on it is good so it can be found easily. Plus, you gotta pay for the hosting and domain (luckily it's gotten pretty cheap depending on where you go).
I personally had one built because my comic is created by a team and we are a legit company. I also go to a lot of events/conventions and do a fair amount of networking, so I was getting tired of handing someone a business card with 7 different links on it or having to tell someone, "yeah you have to go to this site called Tapas.io and search 'Midwinter'". Way easier to just say, "Everything you need to know is on midwintercomic.com!" and it sure did streamline my business card design.
So, the plus sides of having a website is: better branding, professionalism, having a hub where everything is, being in control of how your comic is displayed, and not being screwed if your main hosting platform goes down.
At the end of the day it's just up to you if it sounds worth it and if you have the time and patience to do it yourself or the money to hire someone!