There are several reasons why it's beneficial, from both a UX and a business point of view.
The main UX reason being - not all email clients can handle HTML emails. This is less of an issue these days but it's still a fact. There are hundreds of email clients out there, on loads of different devices. Some browser-based, some OS based, some 3rd-party client based, in-house corporate ones... You have no idea what email client people are using. And you also have no idea if they've opted to disable HTML emails themselves, which a quick Google search shows is something people do want to do. If these people don't have HTML emails then they won't be able to activate your service. Plain text links negate that risk.
And from a business perspective it's risky to leave these out too. Sending emails in pure HTML is a trigger for some spam-detectors who will just block the email outright.
You'll probably still reach most of your target audience with HTML. But reaching 'most' isn't as good for business as reaching 'all' (or as close to all as you can get).