This strategy is an alternative to PESOS (Publish Elsewhere, Syndicate (to your) Own Site) [0]. I really like this read on the indieweb website, it explains well why adopt this strategy for federation and emphasizes that "Friends are more important than federation", something a lot of nerds and hackers forget when defending their ideals.
You can have both! POSSE to post multiple places. PESOS to pull in anything posted directly in other places, i.e. anything that didn't originate from a POSSE post.
[0]: https://indieweb.org/PESOS