The objection to a carousel is really an objection to the reasons that people use carousels--to satisfy a few high-maintenance stakeholders, whether internal or external. But satisfying high-value stakeholders is a real business goal on a lot of websites. Carousels are a great way to manage that.

People also tend to overstate the negative impacts of carousels because they have not internalized the patterns of search and social traffic. On the websites I manage, 80-90% of visits do not start on the homepage! So only a very small number of visitors are actually seeing the carousel at all.

Most homepages today are really just another landing for a particular subset of your traffic. You'll get people who are totally unfamiliar with you, and need an intro. Or you'll get people who are intimately familiar with you and want to see if their pet thing is important to you--a good fit for a carousel.

Carousels are for promotion, not navigation, so task-oriented usability studies are not really applicable. Online promotions deliberately reduce usability in the interest of capturing attention.