You don't have to "build" anything. Just have a button "cancel subscription" with a mailto: link... or even some text saying "email us at @ from your account and it will be cancelled within N hours/days".

Currently what most companies (including startups) do is burying the cancellation instructions in some Knowledge Base, or forcing some back and forth via email or phone.

You can rationalise bad behaviour all day, but we all know very well the reason people don't make it easy to cancel.