Because ee.co.uk.billing.info would get taken down pretty quickly. Using this method the domain only has to work for one day before they move on to the next one.

Because even if you could buy billing.info it would get blocked pretty quickly.

In addition to the sibling comments, there's also the problem of having an actual slash in your example, which may cause the mark to notice it and therefore notice the "missing" slash after the 'co.uk' part.