But note it's at the expense of a very large index file - 800MB (vs Mongo's 100MB). Although Pg's index covers the entire JSON structure, whereas Mongo's index only covers the leafs being searched, so it will optimize a larger variety of queries.
GIN indexes are big, but Mongo's indexes are bigger than all other PostgreSQL indexes, and Mongo also requires much more space for the data.
Such large indices also limit how many of them can be stored in memory at the same time - making transactions against those indexes slower over time if the indices have to be loaded and unloaded from memory frequently.
You should always choose indexes with care, because indexes not only cost space, they cost time. And as you said, Time is expensive.
This is why MongoDB recommends all indices fit in memory