I don't need to apply additional flux. What's in the solder is plenty.
Monkeh nailed it again. When you tack down that first pad (tin pad, heat, move on), then you need to come back and reflow it, and for that you really should either add flux, or add more solder which includes flux, and either way makes a mess. If I had a couple more hands, I could skip tacking it down and just solder it properly from the outset. With paste, I have one additional hand free to hold the part in place because I don't need to feed wire.
Definitely not worth a stencil. The reason it's much faster is that I can do it in batches. As Monkeh said, doing them with just an iron and solder has you forever picking up and putting down different tools and things. With the paste, it's
1) goop a batch of boards
2) place parts on a bunch of boards
3) hold down with tweezer, and touch with soldering iron
It doesn't seem like it would save much time but it does.
One day, I'll convert most of the components over to surface mount and just have them populated the modern way, but I don't like doing that until a design has been stable for a while. I'm forever tweaking things for customers, and using old boards to prototype new designs. That's much harder to do surface mount.