No way does any beer get thrown out,save for that couple of tablespoons left in the bottom. I made my own bottling bucket with the Italian red/white spigot a bit closer to the bottom than what is normally seen. I get all but that couple TBSP out by tiping it slightly. And since I rack clear beer to it,theres only a smattering of grainy bits in the bottom anyway.
Now here's how I avoid the air constantly getting into the tubing connecting the bottling wand to the spigot on the bottling bucket. I leave a long tube so I can sit a bit away from the BB & set bottles on my old 12 pack cooler.
I set 2 or 3 bottles on top of the flat top cooler,then hold the bottling wand in a bottle,but not pressed against the bottom. I then turn on the spigot on the bottling bucket. Pressing the wand against the bottom to open the pin valve & start filling the bottle. By this time,the beer has already started filling the tube to the wand. This is set up on my right,a chair with the full bottle tree/vinator on my left. so I can grab bottles with my left hand as I'm filling with my right.
Now,here's where things change from the norm. If you shut the spigot off to stop & cap bottles,it sucks back air into the tube/wand assembly. So I just don't do that. The bottling bucket is usually to the right of another FV with a spigot on it. The bottles on the cooler below that FV.
So I prop the tube over the FV's spigot,the end of the wand suspended in an empty bottle,but off the bottom. The wand is shut off,& has an empty bottle to drip in while I cap the filled bottles on a low table in front of me.
This way,the spigot stays "on" & no air gets into the wand/tube assembly. The liquid coming into the tube & wand keeps enough pressure on it to avoid suck back of air into them. You can see this in use on my youtube channel,also "unionrdr". I have a two part bottling video on there.