How do some researchers have such beautiful figures in publications, while their homepages look simple? Do some PIs who publish in Nature, Cell or Science collaborate with professional designers?

The thing is that I have never seen it mentioned in their work. Is it a service offered by the journals? Or do the PIs pay for these services and outsource them?
There are a few reasons not to waste time with web design:


academic web pages are read mostly by other academics who are looking for information;
the information a professor needs to put on pages is about group members, papers published and talks, courses, books and none of these seems to require sophisticated web design skills;
learning proper web design skills is time taken away from research. Most professors don't have that time. But, it can happen that graduate students or postdocs are capable of making nice web pages, so the professor asks them to do that. 


The beautiful figures that appear in journals, are most often the work of postdocs and graduate students. Again, most professors won't spend time making them, unless they can't rely on anyone else. It was quite common back in the day to have someone else from within the university or research institute make figures and typeset, but now, there are plenty of great software packages one can use to make figures.