Actually, not anyone with an email server can do it. That's literally MailChimp's value proposition - that they have servers that are trusted by the major email providers and so have high delivery rates. In order to compete with them, you must ensure that your servers are similarly trusted - the process by which this happens being an undocumented black box that is different for each email provider, which often involves having personal contacts at those providers.
In other words - there's a high barrier to entry and you can't provide the service at all if you don't have a certain amount of volume to make a certain amount of profit to cover operating costs. Targeting a niche will not provide that volume.
