MailChimp's a rare one. Being funny at all is hard to begin with, even more so when it's only written, and even more so to a large, broad group of people. It can be exclusive too; references / memes people don't get just create confusion, and implicitly tell people that your service is not for them. MailChimp uses a light, upbeat tone much more than they use outright humor.
Additionally, the reward is not worth the effort for most startups. Email marketing tools are pretty interchangeable from a features standpoint, so MailChimp's brand is more important for conversion and retention than it would be if it were a different type of service.
For most startups, you're better off differentiating with value than you are with personality. But if you already have that covered or are in a commoditized market like MailChimp, some other examples to check out are: