The advantage of EPS over PDF? And why so many journals ask for EPS alone? I have been curious about why so many journals only accept EPS for vector graphs rather than PDF.

It is indeed weird because these journals have to convert EPS figures to PDF anyway. Adobe also suggests to use PDF instead of EPS.

For me, EPS is much hard to view and process than PDF. Does EPS makes a journal editor's life easier? Why?

In addition, as far as I understand, PDF is an open standard format that is free to anyone (relative sure), while EPS is copyrighted by Adobe (not very sure).
The eps format used to be the only possibility for including graphics in (La)TeX. Now the more modern alternative is using pdflatex, which also supports other more common graphic formats natively (such as pdf).

Most journals have outdated LaTeX processing pipelines, so they are still using eps. (And, frankly, they have little incentive to get more modern, since they are in a strong oligopoly position.)