I think there's too much emphasis being placed on employing a bottling bucket as being extra work or a risk of some sort. That's not factual. Once it is empty, it takes about two or three minutes to clean--maybe--but probably less. It's an insignificant amount of time and effort and using one doesn't increase the risk of contamination as long as it's sanitized just like everything else is. If it does increase the risk, you're doing it incorrectly. Any activity requires some effort to do things correctly.
Since this thread leans toward basic bottling, there's no need to discuss the very slight amount of oxygen--which no one would be able to detect flavor-wise--incurred by using a bottling bucket.
I've read claims of crystal-clear beer when batch priming from the FV. That may be true; however, my experience is that one jiggle of my FV and the yeast kicks up and it doesn't settle anytime soon. Relying on yeast with high flocculation would be limiting.
Basically, I'm speaking up here because some of the info in this thread could give an inaccurate impression to new brewers on the subject.
Of course, if someone wishes to stir the primary after adding priming solution and they get great results that's fine, but it won't work 100% of the time for all beers and all yeasts. Using a bottling bucket and batch priming (or bottle priming) will.